I mean, twin stick gamepad or to lesser extent touchpad just isn't going to be as good as a mouse for an FPS. A good mouse player will beat a good touchpad or gamepad player.

And the problem with the Deck is that it has a PC game library, and a lot of those are designed with a mouse in mind. Console FPSes usually adjust the game difficulty so that playing with twin sticks are practical. Enemies give you more time to slowly turn around without inflicting enormous amounts of damage. Auto-aim assist is common. Ranges are shorter. Stuff like that.

If this is a single-player game -- which it sounds like you're playing -- you can reduce the difficulty to compensate for the input mechanism.

There's an input mechanism that some people developed for twin-stick gyro controllers called Flick Stick, which someone else mentioned; Steam Input supports this. The mouse is still going to win, but it's an improvement over traditional pure-stick input.

There's also some input mechanism which I think was different from the "Flick Stick" approach -- though maybe I'm wrong and misremembering, didn't have an interest in exploring it -- that IIRC someone put together using Steam Input. The way it worked, as I recall, was that one could tap the thumbstick in a direction and it'd immediately do a 90 degree turn. The idea was to provide for a rapid turn while keeping sensitivity low enough to still permit for accurate aiming. But I'm not able to find the thing with Kagi in a few searches, and it's not impossible that I'm misremembering...this was only a single video that I'm thinking of.

I don't think that there's any trick to learning this, just playing games and picking it up over time. I mean, I was atrocious at using a keyboard+mouse when I first started doing it, and ditto with twin-stick FPSes.

You could also attach a keyboard and mouse, though I think that that kind of eliminates the point of the Deck, at least as long as one also has a PC to play on -- it might make sense for someone who just uses a Deck and a phone.

is there an easy FPS game where I don’t have to move or shoot too fast

Play games that are designed for consoles or which have a gamepad mode, rather than a keyboard+mouse PC game. They'll be tuned for controller limitations. Like, can you play Halo comfortably with the Deck? That was designed for a gamepad originally, and it's available on Steam (though I'd note that it requires a Microsoft account, which you may-or-may-not be willing to do).

https://old.reddit.com/r/truegaming/comments/8f7oyr/the_core_reasons_thumbsticks_are_inaccurate/

This also talks about some limitations of thumbstick aiming (if you're using thumbsticks and not trackpads). It might be possible to tweak some of these, like sensitivity or dead zone, but I'd assume that for a given game, the developers have already chosen pretty reasonable defaults.