You can play CAT & ONION on Steam Deck (and Linux)
The game runs smoothly and shows the correct button icons
WARNING: The only issue is that the native Steam Deck/Linux version has very occasional crashes. I am looking into this, but you can work around this by using the "Proton 9.0 (Beta)" compatibility tool. Enable it by going into the properties of game on Steam, go to the "Compatibility" tab and then check "Force the use of a specific Steam Play compatibility tool". In the drop down select "Proton 9.0 (Beta)"