A lot of great games have already been mentioned. Here are some options that I don't think anyone has mentioned yet:

• Assault Android Cactus - twin stick shooter (to access the start menu, you must be inside of a stage, not in the map)
• Jamestown - bullet hell (get original game, Jamestown+ does not work on Steam Deck)
• Broforce - 2D side scrolling action game (there's a free version, Expendabros, that you can try out)
• Gauntlet - dungeon crawler
• Guns, Gore & Cannoli - side-scrolling shooter (it plays on Steam Deck, but throws an error when you exit, so you might have to close it directly on the Steam Deck or mess with compatibility options, I'm not sure)
• Hammer Watch - dungeon crawler (need to grab a community controller layout - there is one specifically for co-op)
• Monaco - stealth co-op heist
• Human Fall Flat - physics puzzle adventure
• Wizard of Legend - roguelike
• Divinity Original Sin - turn based rpg (might want to check out the second entry as it is supposed to be even better)

These games are in my backlog and verified on Steam Deck, but I haven't played them yet:

• Children of Morta - roguelike hack and slash
• Darksiders Genesis - hack & slash adventure
• Huntdown - 2d sidescrolling shooter