As a reference point to others: I have a massive Steam library (>300 games) and every game marked as "Verified for Steam Deck" (~20%) worked out of the box. I also played many games marked as "Playable" (e.g. Fallout New Vegas) which also worked perfectly without any specific configuration.

I also had no issues with stability and the Steam Button was a reliable way to get me out of the game whenever I misconfigured something or started a game with "unknown" ranking, which actually didn't work.