The released game is single-player. Steam lists Single-player; PlayStation lists one player, and Nintendo lists one player on a single system. There is no advertised online co-op, local co-op, split-screen or cross-platform multiplayer mode in these official listings.
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Save data and platform boundaries
Crossplay means people on different platforms playing together. Cloud saves and demo-save transfer concern saved progress instead. Steam Cloud or Nintendo Save Data Cloud therefore does not prove crossplay, and the demo-transfer announcement does not promise universal cross-platform saves.
Future multiplayer plans
The October 2 development update discusses balance, workstations, zombie helpers and other improvements. It does not announce a multiplayer release date. Requests from players are not a confirmed feature roadmap, and an unverified mod is not an official supported mode.