Home compatibility for Pokémon Scarlet and Violet released on May 30th with Home's 3.0.0 update.
Pokémon HOME will soon be updated to version 3.0.0 and players will be able to link Pokémon HOME with Pokémon Scarlet and Pokémon Violet. Linking Pokémon Scarlet or Pokémon Violet to Pokémon HOME will allow players to move Pokémon freely between Pokémon HOME and their game—just remember that Pokémon can only be moved to games that they appear in. For example, Dolliv cannot be moved to Pokémon Sword, Pokémon Shield, Pokémon Brilliant Diamond, Pokémon Shining Pearl, or Pokémon Legends: Arceus because it does not appear in those games. A Pikachu from Pokémon Scarlet and Pokémon Violet, however, can be moved to those games because it appears in them. Additionally, the Tera Type of Pokémon moved to Pokémon Scarlet and Pokémon Violet will be determined by their original type or types.
> You can celebrate this new connectivity between Pokémon HOME, Pokémon Scarlet, and Pokémon Violet by receiving a special gift! When you transfer a Pokémon from Pokémon Scarlet or Pokémon Violet into Pokémon HOME for the first time, you’ll be able to receive a Sprigatito, Fuecoco, and Quaxly with Hidden Abilities as Mystery Gifts in the mobile device version of Pokémon HOME. Bring them into your game and have even more fun on your adventures in Paldea! (These Mystery Gifts can only be claimed once per Pokémon HOME account.)
> You will also be able to bring Roaming Form Gimmighoul from Pokémon GO into Pokémon Scarlet and Pokémon Violet via Pokémon HOME.
Source
A list of all Pokemon you can transfer to Scarlet and Violet (at the time of typing) can be found here.
