It has been confirmed that, from Version 1.3 update that drops tomorrow, if you have a save file of Pokémon Legends Arceus that has completed the main story missions, you will get the Azure Flute item in Pokémon Brilliant Diamond & Shining Pearl. This will allow for you to catch Arceus in the game. You get the Azure Flute item from your bedroom in Twinleaf Town
In addition to that, from April 1st 2022 at 06:24 UTC through April 30th 20:28 UTC, you will be able to receive the Member's Card through Mystery Gift to encounter the Mythical Pokémon Darkrai