Following an update later today.
Both Arceus and Darkrai are coming to Pokémon BDSP later today as version 1.3.0 is rolled out.
To obtain Arceus you’ll need a save file of Pokémon Legends Arceus on your Nintendo Switch system and have all the main missions complete. In Pokémon BDSP you’ll need to have entered the Hall of Fame and obtained the National Dex. If you’ve done that go to your room where you’ll find an Azure Flute. Go to Spear Pillar on Mt. Coronet and Arceus will appear!
To obtain Darkrai you’ll need a Member Card item—available between the new moons—via the Mystery Gift feature in Pokémon BDSP. For this Pokémon you’ll also have to registered in the Hall of Fame and obtained the National Dex. When you’ve obtained your Member Card you can travel to Newmoon Island where you’ll encounter Darkrai.