In total, that would account for more than 1,000 different Pokémon and their forms. However, that doesn't seem to be the case. Serebii is reporting that trainers need to have all 890 Pokémon ...

Only the most dedicated Pokemon players can achieve the feat of getting a rare Poke Ball-colored Magearna in Scarlet and Violet. Completing the National Pokedex up to Galar, catching all 890 ...

is by completing the National Pokedex in Pokemon Home all the way up to the Pokemon Eternatus (#890), which also includes every single Mythical Pokemon in the Pokedex up to Melmetal (#809).