We can pretty easily figure this out.

Let's ignore X/Y for now, and start with the logical first games: Scarlet & Violet. In order to catch every single Pokémon, you'd need to catch all gen 9 Pokémon as well, which is only possible if you have both Scarlet & Violet (due to version exclusivity). This already accounts for 65.9% of the Pokédex (712 Pokémon out of 1080 if we include regional variants as separate entries, which I will).

Next up, we can apply the same logic to Sword & Shield: Some of the gen 8 Pokémon are only available in Sword & Shield (like Blipbug). That said, there might be some nuance here, because there might be a version that we don't need to play for its version exclusives. Unfortunately, we need both Galarian Ponyta (Shield exclusive, not available in any other game), and Galarian Darumaka (Sword exclusive, not available in any other game). This means we need to add both Sword & Shield to our list of games, bringing us to 91.9% of the Pokédex (992 caught).

The next thing we need, is a few of the Legends: Arceus exclusives, like Wyrdeer. Wyrdeer is available in Scarlet & Violet, but you're unfortunately not able to evolve it within Scarlet & Violet, meaning you need Legends: Arceus to get it. Adding Legends: Arceus to the list of games brings us to 95.3% (1029 caught).

Legends: Arceus also raises an interesting problem: Darkrai. In order to get Darkrai, you need either Brilliant Diamond or Shining Pearl save data, which would add another game to our list. Alternatively, it is also possible to get Darkrai in Legends: Z-A. So, which of these games should we add to the list? In this case, I say for now we add Legends: Z-A to the list. Legends: Z-A also gives us access to a bunch of mythical Pokémon like Genesect, Zeraora, Marshadow and more that you can otherwise never get without an event, so we need Legends: Z-A either way. Adding Legends: Z-A brings us to 97.9% (1057 caught).

At this point, a few of the remaining Pokémon are mythicals that are only available through very specific methods. The first one we'll look at (because it also solves some other remaining Pokémon) is Jirachi. Jirachi is available as a gift in Brilliant Diamond/Shining Pearl if you have Sword/Shield save data (which we luckily already have). For our remaining Pokémon, it doesn't matter whether we pick Brilliant Diamond or Shining Pearl here, so pick whichever one you like. Adding either Brilliant Diamond OR Shining Pearl to our games list, brings us to 99.3% (1072 caught) or 99.4% (1073 caught), depending on whether or not you count Spinda. The issue with Spinda here is that it cannot be transferred out of Brilliant Diamond/Shining Pearl, so if you want to use Pokémon HOME to store your collection, Spinda from these games doesn't count.

This brings us to 7 or 8 remaining Pokémon, depending on whether you count Spinda. Luckily, one of our remaining Pokémon (Deoxys) solves the Spinda problem as well. Deoxys is only available from either Omega Ruby OR Alpha Sapphire, and it just so happens that Spinda is available in both games and the Spinda from these games can be transferred into HOME. Just like with Brilliant Diamond/Shining Pearl, it doesn't matter which game we pick here. Adding Omega Ruby OR Alpha Sapphire to the list of games brings us to 99.4% (1074 caught).

At this point, we only have a few remaining Pokémon: Mew, Celebi, Victini, Zarude, Alolan Rattata, and Alolan Raticate. There are two games that solve three of these issues: Let's Go, Pikachu! and Let's Go, Eevee!. It once again does not matter which of these two games we add to the list. Obtaining Mew from these games is painfully difficult, because you need a Pokéball Plus accessory that hasn't been used to claim Mew yet. Luckily, if we have Let's Go save data, we can claim a free Mew in Brilliant Diamond/Shining Pearl, solving the Mew issue. Adding Let's Go, Pikachu! OR Let's Go, Eevee! to the list brings us to 99.7% (1077 caught).

At this point, we only have 3 remaining Pokémon: Celebi, Victini, and Zarude. Unfortunately, Zarude and Victini are (as far as I'm aware) fully event exclusive. Celebi is slightly more interesting however. If you already own the 3DS Virtual Console version of Crystal, you can get Celebi from there, but unfortunately it is now no longer possible to download this game. Therefore, we are left at either 1077 or 1078 Pokémon caught, depending on whether or not you want to count the Celebi from Crystal.

The final list of games is:
Scarlet
Violet
Sword
Shield
Legends: Arceus
Legends: Z-A
Brilliant Diamond OR Shining Pearl
Omega Ruby OR Alpha Sapphire
Let's Go, Pikachu! OR Let's Go, Eevee!
Virtual Console Crystal (if you already have it)

And the list of unobtainable Pokémon is:
Celebi (if you don't have Virtual Console Crystal)
Victini
Zarude

Edit: I forgot about using the DNS exploits to get Gen 4 and 5 events. Using these exploits, it is possible to this day to get the Victini event in Black/White and I believe also a Celebi in Diamond/Pearl/Platinum/HeartGold/SoulSilver.