According to the developer:
You may notice that Steam marks the game as ‘Unsupported’ for Steam Deck. This is due to the Legends co-op multiplayer mode requiring Windows to access PlayStation Network integrated features.
They’re rolling out a new in-game PlayStation overlay that requires PSN and windows to work, and multiplayer features won’t be available without the two. It’s possible that Valve will be able to fix the windows incompatibility issue, although there’s no hope for the PSN requirement part being removed.
Wow, wtf? So far Sony’s been good to the Deck, and while I don’t mind the psn requirement (when it’s upfront!) this seems either dumb or somewhat of a slip up. Hopefully someone will fix this (either Sony with an update to lose the Windows dependencies, or Valve with Proton sorcery). It is after all in Sony’s best interests to not encourage people to use systems from their competitors, so supporting Linux would make sense…