There's quite a limited amount of information to go by with context, but it's possible that the issue is with multi-input.
Most games are not designed to use both controller input and mouse + keyboard input simultaneously which means using joystick to mouse or any other mouse input to require your entire controller to use mouse + keyboard bindings (such as WASD for left joystick, etc) because the game is not optimized for what you're doing.

Imagine the game sees your mouse moving but switches from your mouse to joystick camera while you're moving your character around. The input is taking a few MS or more to switch between inputs.

Yeah I've thought about that, but it seems to do it with strict K&M on pure PC games as well, actually especially with those. It's really hard for me to identify the root cause of it, I've been trying for months, avoiding to create an issue, but I felt like I had to at some point.
Maybe it's related to input layers as well? It's really hard to tell I'm sorry.

Your best bet is to start with simplifying everything. One important factor to consider is that if the issue doesn't occur with the joystick, the mouse input shouldn't change much outside of faster input which might affect culling / load. That being said, this is why multi-input is a very likely culprit. Maybe even try plugging in or setting up a Bluetooth mouse and keyboard to find out if it's an input issue.

Create a new controller profile. You can attempt to use the Mouse and Keyboard template which removes all standard controller bindings but you can go as far as unbinding everything completely and only using the mouse input. If the issue still occurs, that helps you narrow out multi-input issues.

If the issue still occurs, you can try setting everything to lowest settings and resolution to identify if it's possibly performance related.

Try in desktop mode to figure out if it's related to SteamOS. You can attempt running the Konsole and run FlatPak update to check for additional updates.

If it still continues to happen, you may want to run advanced steam performance monitoring to identify if there's a CPU or GPU usage problem. If the game is offloaded to an SD, you can attempt using the onboard SSD. A recording of the issue might also help because some stutters are easier to identify the issue based on how it stutters.

There was a major push that was made on the stable SteamOS branch recently, and I saw many occurences in the changelog mentionning the compositor and frame delivery, and how it would apparently fix things mostly for VRR.
I'm not sure what changes were made under the hood, but it seems to have completely fixed the presentation pacing issues the Deck had for a while (9 months+!) now! Now every game that can maintain the target refreshrate have perfect presentation and it's amazing, I'm so happy!

Now we only need the ability to restore the "allow tearing" functionality for latency enthusiasts!