You'll be able to play any game that can be run on Proton (Valve's Linux compatibility layer). Technically, you can install windows on the deck and then run anything on that, but that's not supported out of the box.

You can look at a list here for what Steam labels as "Deck Verified" https://www.steamdeck.com/en/verified

Additionally, you can look on protondb which is similar to the above, but takes input from users and may have additional notes on compatibility: https://www.protondb.com/explore?selectedFilters=whitelisted

Performance and battery life will depend on the game, but there's a ton of videos and benchmarks if there's a particular game you're curious about.