With the update of Pokemon Home 2.0.0, Pokemon can now be sent from Brilliant Diamond and Shining Pearl (BDSP) and Legends Arceus (LA) to Home and back. However, certain restrictions have been put in place that greatly affects how communication with BDSP works.

Mainly, you may only transfer 1x of each Legendary or Mythical from your own BDSP save file to Home and back. For example, by transferring an Arceus from your BDSP save file to Home, you cannot transfer any other Arceus to Home from the same save file. You may transfer an unlimited amount from Home to BDSP, but not the other way around.

This means that if you are looking to eventually move your own Pokemon obtained through your playthrough to Home, but have also purchased Legendary or Mythical Pokemon from Rawkhet, you may want to prioritize accordingly what you will end up moving into Home.

A full list of additional restrictions can be found on Serebii here.