Wargroove will be Available on the PS4 This Week, and Will not have Cross-Play
The PS4 version of Wargroove will have all the features found in the Nintendo Switch, PC, and Xbox One versions of the game, except cross-platform play.
They are Billions out now on PS4 and Xbox One, no story campaign for now
Survival mode is available but the They are Billions campaign called the New Empire is not available on the PS4 and Xbox One version right now.