Can a PS5 player and an Xbox player share a session?
Crossplay is a property of a multiplayer mode. It describes whether players on different machines can occupy the same session. No online mode has been announced, so there is no session to share, and nothing for crossplay to be true or false about.
That is not a way of avoiding the question. It is the answer, and it stays the answer until an online component is announced — at which point this becomes a live question with a real answer, and this page changes.
Cross-progression is a separate question with the same answer. Crossplay is about sharing a session with somebody on other hardware; cross-progression is about carrying your own account, save or character between machines. Nothing published names either one: no announced save transfer, no announced account linking, and no announced entitlement that follows you across storefronts.