You can genuinely feel just a few milliseconds of input latency with a mouse, it disconnects looking around with your physical actions. It's the same way you can feel the difference between low and high refresh rate monitors, even though you can't really count the frames themselves

It doesn't matter. Whether you have a ping of 40 or a ping of 300, 3ms is 3ms and will mean you win a little less often.

The saying we have in bike racing marginal gains is "leave no stone unturned, but turn over the big ones first"

So sure, first make sure your internet connection is solid. Then make sure your hardware and game settings are optimizing FPS to a reasonable point of diminishing returns.

Then make sure you don't use XWayland