I've not found many instances where performance in terms of frames per second is worse. If anything on linux it's more stable with less dropouts.
But, for whatever reason there's definitely more latency (NVidia 3080 here) when playing for example CS:GO (not tried since CS2 though) on Linux compared to Windows. Not sure where it is being added (possibly the compositor?) but it is definitely noticeable. If I move from playing on Linux to windows I'll overshoot when aiming for example.