I'm currently running latest Archlinux with all drivers up 2 date on my Desktop(Ryzen 3600, 16GB Ram, GeForce 1070 Ti), but it also happens on Holoiso or the Steamdeck.
The native linux version has 1-2 seconds input delay on every control input type.
regardless if i try to use gamepad or mouse & keyboard.
I have my constant 165fps (locked to display refresh rate) but the input is very delayed.

This doesnt happens with the Windows version which i run via Heroic Launcher & Wine-GE-34

I did experience that, I think it comes from NVidia graphic drivers as I don't have the problem anymore since I switched to AMD GPU.

I remember the solution I found at the time was to simply disable vsync.