This page is our investigation of cross-play game Deep Rock Galactic. We always verify information manually using official sources - no AI.
Information about cross-play support between PlayStation 4 and PlayStation 5 can be found on the Deep Rock Galactic Steam News page here. It says that with a release on the PlayStation platform in 2021 game will have cross-gen cross-play.

Yes, Deep Rock Galactic supports cross-play, but only partially. Only players on Xbox One, Xbox X|S, and PC (via Xbox Store) can play together.
The information about cross-play in Deep Rock Galactic was taken from the official game website. You can check it for yourself by following this link.

To clarify: players who bought the game on Steam won't be able to play with those who bought it on the Xbox Store. Players on PlayStation can play only with other players on PlayStation 4 and PlayStation 5.