There will be 4 groups of games that are compatible with Pokémon Home after Pokémon Legends Arceus is released. Strangely enough, the only starters that have yet to be confirmed for any game are the ones from the Kalos region as seen below:

Kanto: Let's Go/SwSh/BDSP
Johto: BDSP/LA (Only Cyndaquil confirmed)
Hoenn: SwSh/BDSP
Sinnoh/Hisui: BDSP/LA
Unova: LA (Only Oshawott confirmed)
Kalos:???
Alola: SwSh/LA (Only Rowlett confirmed)
Galar: SwSh

In addition, Snivy and Tepig have not been confirmed to be in any games yet. Is it safe to assume all the missing starter Pokémon will show up in Legends Arceus? This also assumes only Pokémon from generation 1-4 will appear in BDSP.