Soon you will be able to link Pokémon Legends Arceus, Pokémon Brilliant Diamond and Pokémon Shining Pearl to Pokémon Home. This means you will be able to deposit and withdraw Pokémon to and from each of these games along with Sword and Shield. With this version 2.0.0 update Pokémon Home will have access to each Pokédex from each game. 

Here is an image on how everything is linked now:

If you wanted an example, if you had caught a Zacian from Pokémon Sword and wanted to deposit it into Home to be transferred to Pokémon Legends Arceus, you can now do that with this update. 

Other information coming from the official Pokémon blog post is that you will be able to obtain special Pokémon if you transfer from each of the new added games.

When you deposit a Pokémon from Pokémon Brilliant Diamond or Shining Pearl to the Nintendo Switch version of Pokémon Home, you will receive a Turtwig, Chimchar, and Piplup with hidden abilities as Mystery Gifts in the mobile version of the Pokémon Home app.

With Pokémon Legends Arceus, when depositing to Pokémon Home you will receive Rowlet, Cyndaquil, and Oshawott with maximum effort levels as Mystery Gifts. 

There has been no date set yet on when this update will be released.

You can find all the information here.