apex legends works. the finals does not, because of their anti-cheat solution.
for multi-player fps games remember that you'll play against pc players, they'll have keyboard and mouse and you won't have assistance features you might be used to from console fps. Experiment with gyro controls, the touchpads and/or "flick stick" you'll might find a way to get similar speed and accuracy as a mouse user, but i'd guess you are in for an uphill battle.
have a look at the control schemes provided by the community for games, if you don't like the default controls.
my competitive fps days are in the past, but i can recommend some single player fps i enjoyed on the deck:
- Doom (2016)
- Black Mesa, the half-life 1 remake.
- Amid Evil
- Boltgun
- Borderlands 2
e: www.protondb.com to check how various games work on the deck. some games are not "verified" by valve because they only show xbox button prompts, or some "unplayable" games run perfectly fine with a specific launch options