Some Pokemon can't be gotten from just finding them in the Overworld, Some can't be found from Outbreaks, and some can't be obtained from Raid Dens (unless they are/were event dens). I dont know if anyone has made an extensive list like this or not, but I decided I'd try to be nice to those who don't want to scroll through all of the Serebii pages.
​
Version Exclusives: This may be best to start with, just so people know and aren't trying to find things they can't in their game: https://pokemondb.net/scarlet-violet/exclusive
Not from any: The only Mons that can't be found in any of the methods listed are the Starters (Sprigatito, Fuecoco, and Quaxly), their evos, and Gholdengo. Trading for all the starters is needed. Gholdengo needs all 999 Coins to evolve Gimmighoul, and be added to the Dex.
Not from Encounters or Outbreaks (So Raids Only): Annihilape, Slowing. Muk, Gengar, Scizor, Tyranitar, Salamence, Krokorok, Krookodile, Haxorus, Kingambit, Hydreigon, Goodra, Coalossal, Flapple, Appletun, Polteageist, Hatterene, Grimmsnarl, Dragapult, Pawmot, Maushold, Arboliva, Armarouge, Ceruledge, Rabsca, Tinkaton, Palafin, Baxcalibur
​
Static Encounter Only: Dragonite, Cacturne, Spiritomb, Garchomp, Hippowdon, Magnezone, Eelektross, Toxapex, Tsareena, Sandaconda Gimmighoul, and Koraidon/Miraidon
Area Zero Only: Volcarona, Talonflame, Garganacl, Glimmora, Farigiraf, Dudunsparce, and all Paradox Pokemon other than Great Tusk/Iron Treads.
Both Static and Area Zero Only: Braviary, Corviknight, and Great Tusk/Iron Treads
Not from Outbreaks: *Sunkern and Bruxish can not be found via Outbreak! Weird for basically all other base forms to be available except them, but whatever. Because of how Outbreaks work, no Pokemon listed in above categories are also not available in Outbreaks.
​
Not from Encounters: Muk and Krokorok can't be found in the overworld, but Serebii says they can be found in outbreaks. I had thought outbreaks were decided by what could spawn in areas, so if these 2 don't spawn normally, can they spawn as outbreaks? If they can, I'd love to know!
Edit: Apparently they cannot, therefore making it so no Pokemon are exclusive to being caught from outbreaks. These 2 have been move to Raid Only.
​
Not From Raids: Jumpluff, Spiritomb, Lucario, Floette, Salazzle, Palossand, Arctibax, Gimmighoul, and obviously the Legends/Paradoxes. The entire Scatterbug line is also unavailable from raids.
​
I hope this helped people who were looking for specific mons, or wondering why they weren't showing up. People will flame me if I said "maybe Serebii is wrong", so You didn't hear it from me, OK?

So, after playing violet and raiding for a week I've come to the conclusion that 5 star raids specifically lack any real balance and results impossible circumstances at worst, or at the very least is bad content. 4 star and below are easy enough to clear solo with a good Pokémon, and 6 star raids, being the end-game of end-game raids are appropriately difficult for what they are, although I've only done like 5-6 of them successfully. But this post is about the 5 star specifically.
Why do I think this? Here are my top 5 reasons.

1. 5 star raids are unlocked pre-post game BEFORE the Pokémon league, giving the player the idea that they are simply a modest step up from lvl 4s like 2-3 and 3-4 were. The game does NOT tell you that it is in fact an increase to lvl 75 pokemon, which outlevels all other in-game content including the league, the post-league champ fight and area zero content, and the tournament AFTER the credits. My complaint here is simple, don't give players content its impossible to do at the stage you unlock it. Why is it virtually impossible? See complaint 2.
2. In addition to being level 75, these 5 star Pokémon have insane stats, so insane that you not only need a perfect team of max-iv/max-ev lvl 100 Pokémon to pull it off consistently, but even that doesn't work half the time in online battles. How insane you ask? well I'm glad you did because I have some recent examples of how insane they really are. Two matches that came to mind were against a Baxcalibur(ice terra) and another being Orthworm(water terra):

2a. The first one I used a lvl 99 Tinkaton with perfect Ivs and evs, adamant nature because it resists ice and dragon type moves nicely. 270 attack with a steel move with base 160 power + stab. How much damage does this does this do? like maybe 5% hp to the dude. Now, Gigatonhammer being so powerful can only be used once every 2 turns, and only has 5 pp, so the most you can do with it is 25% of the health of the target by yourself. This is insanely low damage in my mind when compounded with all other things you gotta deal with(outlined later). This makes solo impossible with this pokemon, who should shit on this guy 10 ways to sunday with his type in a normal matchup.
2b. Now this second one is equally silly, but perhaps underlines a different issue. Orthworm being a steel type with water terra meant you could either bring bug, grass, or electric to fight it. Having grinded somewhat now that i've been in postgame for 4-5 days now, i decided to bring Leafeon lvl 100,(just assume i'm always using best iv/evs). Now you might say to yourself, ok well Orthworm has 145 base defense, and i'd say yeah that's like insanely good. But of course I only have so many level 100s to choose from and my guy is 25 levels above them and is terra grass with swords dance so i should be able to buff my way to some good damage. Well, boy was i wrong, even after two swords dances, i was doing like 1% of its hp with leaf blade. Now, according to pokemon damage calculator, at +3 to a normal oathworm(it coiled once) 25 levels below me, i'd be doing between 84-99% of its hp depending on the role. So i was doing like 1/84th of the % health damage I would expect, meaning its defense was so boosted that i was doing < 3% of the damage i would normally do to that pokemon.

1. Taking into account these 2 examples which are just a couple of many I could talk about, this next complaint compounds this issue. I just gave examples of how defensively these terra raid Pokémon get insane buffs, but these buffs are offensive as well, meaning that if you get hit by something neutral and not resisted? Yeah you're probably getting 2-3 shot by that. Now I hear some people out there, "just bring something that resists all its moves", yeah...don't worry, we'll get to that later. So...given the hyper offense capability of a lot of these fully evolved pokemon(and god forbid they get a stat boosting ability like coil or calm mind), its finally time to talk about the actual mechanic of terra raids that makes this broken as all heck. Terra raids are real time, meaning that all players move at the same time for their attacks more or less and these inputs are buffered by relative speed against your opponent in order to determine the order of attack. Now, i was all for this system initially, not having to wait for everyone to go through their turn to attack? Brilliant! Except...they gave the terra pokemon the ability to do it also. So...from what i can tell, the tera raid pokemon on every interval (because no turns) will select an attack and hit EVERY pokemon at the same time on your team with it, and it calculates this damage value as if it is attacking a singular pokemon. This causes a few problems with a few different types of moves:3a. So, for those who dont know, moves like rockslide and surf and moves that attack multiple pokemon at once generally have some of their overall damage nerfed on each one individual to balance out the fact it hits everything, where Pokémon only receive full damage from the move when they are the only one being hit by it. Since terra Pokémon however perform their attack on an individual basis rather than a group hit with these moves, that means it is performing the full damage on each pokemon rather than splitting the damage. This means they are basically ignoring the mechanic of damage splitting.

3b. Status moves, oh god here we go. So lets just start off with the obvious, if your opponent has sleep, para, or burn if you are physically, you are utterly fucked. Not only will they hit all players Pokémon with this ability, meaning that they can sleep your whole party in one interval but they can spam it multiple times between your "turn" ( see 4). good luck doing enough damage in the time limit with only 2 of your party doing damage/setting up.
3c. Single target attacks are just that, single target. they are balanced around hitting one person per turn. So obvious problem here when terra raid pokemon can hit 4 pokemon at the same time with a single target attack doing full damage to each of them. Coupled with #2s problem, and this means they are dishing out a crap ton of dps per interval.

1. So...you've seen me use the word interval to take the place of where a turn normally would. And here is my #2 reason that this system is dogshit. First things first, you better select the moveo you wanna do fast, because if you dont guess what your "interval" is getting skipped to play animations for everyone else and the terra pokemon. So pokemon, which is supposed to be tactical thinking now becomes a rush job to think what your next move will be as fast as possible. Now this is more of a nitpick because any good trainer knows what they are going to use most likely, but this next bit is unforgiveable. The timer will tick down even as animations play, and the terra raid pokemon has the unfortunate ability to do multiple things in succession before you are able to choose your next attack. These things include, using a move, removing any debufs, removing all YOUR buffs, putting its shield up, and stealing your terra orb charge. Oh, and the move if these animations are slow enough can cause them to use multiple moves back to back before you get to do anything. Oh what's that? you wanted to choose your attack? Well better wait 30 seconds for these animations to happen. And you wanted them to get one attack in for each one you deal? oh buddy, good luck with that because they might, idk double moonblast with double stat drop ya, or dragondance earthquake ya or my personal favorite, here have a yawn and then do some shit like coil or amnesia. So not only does this system eliminate any fairness in an attack for attack based game it just straight up ignores it. Also, want to terrastalize? well there's 20 seconds off your timer as you have to sit through the whole god dang animation.
   
2. And here we are long last at #5, and is somewhat related to the issue with #2. See, you really really need to resist the opponents attacks while at the same time having good offensive capability that matches the terra type needed to shield break them. Now there are 18 pokemon types in the game, with approximately 324 different type combinations when you take into consideration dual typing. Now not all dual types exists, so lets just call it an even 300, or even better lets just half it to make the point. 150 type combonations you gotta plan for defensively. You know what, multiple types will fill the defensive combinations for multiple types so lets bring that even lower to 50 different combinations that you got to plan for. Now these 50 pokemon that will cover every possible type you need to fight also need to have the correct terra type to fight them. For the sake of expediency, the average number of weaknesses a type possesses is about 3. So, to have all your bases covered to bring the best pokemon for the fight, you would need about 150 different pokemon to fulfill all these roles, and then multiply that number by 2 for special vs physicals users. so...300 different pokemon to cover those bases for perfect coverage. Obviously this is a bit ridiculous in practice, so when someone says, why don't you have that perfect typing for this specific pokemon that is why, i don't have 300 available box spots in my pc. So, they only thing to do realistically is try to get the best defensive coverage you can while still having an offensive threat, which 90% of the pokemon in the game currently currently just don't have. Don't require that level of perfection for content that is pre-post game. Heck don't require that level of perfection except for the hardest of lvl 6 raids. (Rip future charizard attempts)
   

So yes, this was long but I think I've pretty much covered the biggest issues with the lvl 5 raids. Overpowered stats, ridiculous mechanics for attacking, bad interval shenanigans, and many more.
My closing argument is this, I've seen idk how many people just bring 4 legendaries to these raids either on youtube or twitch or whatever to win these raids. They all use metal sound/screech to lower defenses, buff the attack then use the collision course/electric drift move to do big damage. So my point is this, If you need bring a big legendary stat-stick and win most raids regardless of typing with this strategy while almost all other Pokémon struggle to do good even with proper typing and stats, then that is either dogshit game balance or dogshit gameplay.
P.S Protip, if there is a ditto and you are hosting, dont select a stupid legendary for it to turn into, pick a stupid lvl 5 magicarp with splash so people can win the fight in 10 seconds.
I also did a lvl 6 garchomp so i know how to play lol.

Baxcalibur
Dragon/Ice
Thermal Exchange/Ice Body
115/145/92/75/86/87

*EDIT: The current maximum possible HOME GO Dex number is now:

785

(if I missed something, let me know!)

edits:

2023
May 30

• Now that HOME & SV connectivity is available (and the increasing amount of depositable GO pokemon), six Pokémon (Gimmighoul, Gholdengo, Annihilape, Farigiraf, Dundunsparce, and Kingambit) are now available with a Go** mark in HOME, which has increased the Pokémon HOME GO Dex number by 6 to 785.
  
• Sandyghast and by extension, Palossand, was announced to be coming to Pokémon Go; this will increase the Maximum Possible Home Go Dex Number by 2 on June 6.
  

May 5

• Kleavor is now in Pokémon Go, and can be sent to HOME; but a kleavor with the Go mark could already be obtained in HOME by evolving a Go Scyther in Legends Arceus; so this does not increase the HOME GO dex number again.

May 1

• Larvesta and Volcarona were released into Pokémon Go eggs, which increases the maximum possible home go dex number by two!

April 26

• Joe Merrick suggested on twitter that Diancie might have been teased on the banner for Go Fest 2023 due to the pink gems or crystals in the image. However, as a mythical Pokémon, Diancie would not increase the maximum possible HOME Go Dex number.

April 20

• Bounsweet, Steenee, and Tsareena were released into Pokémon Go, increasing the maximum possible HOME Go Dex number by 3!

April 19

• Shaymin was announced to be coming to Pokémon Go on April 20 at 10am local time. However, Mythicals never count toward the Home Go Dex Number, and so Shaymin will not increase the number from where it is.

April 8

• Regieleki was added to the game, thus increasing the maximum possible home go dex number by 1.

April 3

• Cutiefly and Ribombee have both been released into Pokémon Go, and so the Maximum Possible HOME Go Dex Number increased by two!

Mar 28

• Several upcoming Pokémon were leaked but until they are confirmed via announcement or data mining, I’ll just leave the link.

Mar 10

• Regidrago was added to the game, but there have been significant errors with people being unable to join and/or catch. However, as at least one has been sent to home, it has increased the maximum HOME GO Dex number by 1.

Mar 8

• Bruxish was added to the game, and thus increased the Maximum HOME GO Dex number by 1.

Mar 3

• Hawlucha was added to the game as a Mexico-exclusive regional son Mar 1, and thus increases the maximum possible HOME GO Dex number by 1 (thanks for the heads-up cooptimesudoku )

Feb 27

• Added the two newly released Pokémon to Paldea’s list, as they were released in Scarlet and Violet (but not in Pokémon Go)

Feb 1

• Kecleon can now be sent to HOME again as the restriction on it has been lifted (and the HOME Maintenance has ended).

2022

• Added new section thanks to help from relikter: Announced/Datamined/Theorized

 

Out of the current 1010 total possible Pokemon that could be in a Pokedex:

A. (-22) All 22 Mythical pokemon never count toward the Home Go Pokedex number, even if it is available and you send it up. (This includes Meltan/Melmetal!).
B. (-1) 1 Pokemon (Spinda), is currently not able to be sent to HOME even though it is in Go, and would otherwise count towards the HOME Go dex number.
C. (-202) There are 202 pokemon that are fully unavailable to have a Pokemon Go mark, because they (or their pre-evolutions** ) are not yet made available in Go

So, with a little math: 1010 - 22 - 1 - 202=

785 Pokemon that CAN be registered in Pokemon HOME’s Go Pokedex.

**Some pokemon--currently Wyrdeer, Annihilape, Farigiraf, Dundunsparce, and Kingambit--Can have a Pokemon Go mark in HOME even though they are unreleased in Go. This is achieved by sending the pre-evolution Go Pokemon--Stantler, Primeape, Girafarig, Dunsparce, and Bisharp --to another game (such as Legends:Arceus or Scarlet/Violet) and evolving them, before sending them back to HOME.
 

Lists of all Unregisterable Pokemon***

(If a pokemon is not listed below, it can be registered in the HOME Go Dex.)
 
(A) All Mythicals (22) do not count towards the HOME’s Go Dex number
-Mew, Celebi, Jirachi, Deoxys, Phione, Manaphy, Darkrai, Shaymin, Arceus, Victini, Keldeo, Meloetta, Genesect, Diancie, Hoopa, Volcanion, Magearna, Marshadow, Zeraora, Meltan, Melmetal, Zarude
(B) 1 available pokemon cannot be sent to HOME right now
-Spinda
(C) 202 non-mythical pokemon cannot have a Go mark in HOME due to being unreleased (if name bold, it is announced but not yet in the game). (7 + 20 + 74 + 2 + 99 = 202)
(7) Kalos:
-Skiddo, Gogoat, Honedge, Doublade, Aegislash, Carbink, Zygarde
(20) Alola:
-Wishiwashi, Mudbray, Mudsdale, Passimian, Sandygast, Palossand, Pyukumuku, Type: Null, Silvally, Minior, Komala, Turtonator, Mimikyu, Drampa, Dhelmise, Necrozma, Poipole, Naganadel, Stakataka, Blacephalon
(74) Galar:
-Grookey, Thwackey, Rillaboom, Scorbunny, Raboot, Cinderace, Sobble, Drizzile, Inteleon, Rookidee, Corvisquire, Corviknight, Blipbug, Dottler, Orbeetle, Nickit, Thievul, Gossifleur, Eldegoss, Chewtle, Drednaw, Yamper, Boltund, Rolycoly, Carkol, Coalossal, Applin, Flapple, Appletun, Silicobra, Sandaconda, Cramorant, Arrokuda, Barraskewda, Toxel, Toxtricity, Sizzlepede, Centiskorch, Clobbopus, Grapploct, Sinistea, Polteageist, Hatenna, Hattrem, Hatterene, Impidimp, Morgrem, Grimmsnarl, Cursola, Milcery, Alcremie, Pincurchin, Snom, Frosmoth, Stonjourner, Eiscue, Indeedee, Morpeko, Cufant, Copperajah, Dracozolt, Arctozolt, Dracovish, Arctovish, Duraludon, Dreepy, Drakloak, Dragapult, Eternatus, Kubfu, Urshifu, Glastrier, Spectrier, Calyrex
(2) Hisui:
-Basculegion, Enamorus
(99) Paldea:
-Sprigatito, Floragato, Meowscarada, Fuecoco, Crocalor, Skeledirge, Quaxly, Quaxwell, Quaquaval, Lechonk, Oinkologne, Tarountula, Spidops, Nymble, Lokix, Pawmi, Pawmo, Pawmot, Tandemaus, Mausehold, Fidough, Dachsbun, Smoliv, Dolliv, Arboliva, Squawkabilly, Nacli, Naclstack, Garganacl, Charcadet, Armarouge, Ceruledge, Tadbulb, Bellibolt, Wattrel, Kilowattrel, Maschiff, Mabosstiff, Shroodle, Grafaiai, Bramblin, Brambleghast, Toedscool, Toedscruel, Klawf, Capsakid, Scovillain, Rellor, Rabsca, Flittle, Espathra, Tinkatink, Tinkatuff, Tinkaton, Wiglett, Wugtrio, Bombirdier, Finizen, Palafin, Varoom, Revavroom, Cyclizar, Orthworm, Glimmet, Glimmora, Greavard, Houndstone, Flamigo, Cetoddle, Cetitan, Veluza, Dondozo, Tatsugiri, Clodsire, Great Tusk, Scream Tail, Brute Bonnet, Flutter Mane, Slither Wing, Sandy Shocks, Iron Treads, Iron Bundle, Iron Hands, Iron Jugulis, Iron Moth, Iron Thorns, Frigibax, Arctibax, Baxcalibur, Wo-Chien, Chien-Pao, Ting-Lu, Chi-Yu, Roaring Moon, Iron Valiant, Koraidon, Miraidon, Iron Leaves, Walking Wake
 
*** Some non-mythical Pokemon that do not currently contribute to the maximum possible HOME GO Dex number are either officially Announced, Datamined, or otherwise Theorized to be made available soon. Some of these are detailed below; and when the pokemon is released, its corresponding postulation will be removed.

Officially Announced but not yet in the game

• Poipole, Naganandel, Stakataka, Blacephalon, and Necrozma were teased by Pokemon GO on Twitter
  
• Sandyghast and by extension, Palossand, was announced to be coming to Pokémon Go; this will increase the Maximum Possible Home Go Dex Number by 2 on June 6.
  

Datamined info that might signal a Pokemon's approaching availability

• more info as it becomes available

Theorized

• more info as it becomes available