This page is our investigation of cross-play feature in game called Deep Rock Galactic. We also want to mention that - we always put manual efforts to find the precise, valid, and what is more important official information about different game features without using 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.
Games can have different cross-play combinations, for example the game can have cross-play between PC, Playstation 5, Xbox X|S, but not between old generations like: Xbox One, Playstation 4, PC. To avoid any misinterpretations, we group them into so called "cross-play variations".
Any store inside the cross-play variation have a cross-play only with a store in the SAME variation. We also want to notice, that we put into variation not platform, but store + platform. That is required because some games, for example, can have cross-play between a Playstation 5 and Steam, but not Playstation 5 and Epic Games.