God of War Ragnarök from Santa Monica Studio, Jetpack Interactive and PlayStation Publishing LLC has released on PC today and Valve put it quickly through verification for Steam Deck.
The game unfortunately does require a PlayStation network account.
The game has the same PlayStation overlay that's incompatible with Linux, but when playing on Steam Deck the overlay is automatically disabled. Desktop Linux players will need to use the SteamDeck=1 %command% launch option to disable the overlay.
Somehow forcing us to use a PlayStation account and having an unnecessary overlay that breaks the game for Linux users is supposed to get us to buy PlayStations. I'm not a Sony executive though so I'm not sure exactly on the details.