At this time, those who have been playing the new remakes of Pokémon Brilliant Diamond and Shining Pearl are unable to transfer data between their game and their Pokémon Home account, though The Pokémon Company has plans to bring it to the game in the near future.
Right now, the service is compatible with other Nintendo games, like Pokémon: Let’s Go, Pikachu! and Let’s Go: Eevee!, Pokémon Sword and Shield, and Pokémon Bank (from the Nintendo 3DS).
Source: https://www.distractify.com/p/when-will-pokemon-home-work-with-bdsp