It would be compatible
Pokémon Legends Arceus will be compatible with Pokémon HOME in 2022. During a Pokémon Presents presentation, The Pokémon Company announced that the game would be compatible.
...However, the game will include a "trading post" where you can link up with other players. This might also be where you deposit Pokémon to Pokémon HOME.
It's worth noting that even when Pokémon Legends: Arceus gets Pokémon HOME support, this does not necessarily mean that you will be able to transfer Pokémon from this game to Sword and Shield or other Pokémon games.
So, Legends: Arceus would be compatible with Pokémon HOME, but you might not be able to transfer Pokémon from this game to Sword and Shield or other Pokémon games.
Hope it helped.