To be granted a Verified rating - which denoting full compatibility with Steam Deck - a game must first pass four checks: all functionality must be accessible when using the machine's default controller configuration, Steam Deck controller icons must be shown in-game, interface text must legible on the display screen, and the default graphics configuration must perform well.
Out of the initial 67 titles currently rated, 39 have passed with flying colours to receive a Verified rating, while 23 have failed at least one test, pushing them down into the Playable category. Valheim, for instance, is noted as sometimes showing mouse, keyboard, or non-Steam Deck controller icons during play, while Subnautica loses a point for the fact some functionality isn't accessible with the default controller configuration - instead requiring the use of the touchscreen, virtual keyboard, or a community configuration. As for The Witcher 3: Wild Hunt, "some in-game text may be small and difficult to read".
Of the five titles currently listed as Unsupported, four aren't much of a surprise given they're designed for VR headsets. However, the one oddity arrives in the form of Persona 4 Golden, with Valve merely noting it's still working on adding Steam Deck support for the game.
It appears Valve has been periodically updating its database with new Steam Deck compatibility ratings throughout the day, so while I've detailed everything available at the time of writing below, expect that list to steadily grow. With 67 Steam games down and approximately 50,000 more to go, however, I probably won't be updating the list to completion.