Apparently, all you need to do to "git gud" in an online FPS is to reduce hand "stress" while aiming.

Long, short story:

Am bad-to-average FPS gamer, looking to improve. Saw an OSU! gamer flinging its "shots" left and right and tried my best to mimick the experience in an FPS. And it worked significantly -- all of my shots felt more "secure", even with my aiming being rusty beyond belief.

And the "trick" to do this is simply leaving your "aiming hand" to aim (ONLY) while leaving your "non-aiming hand" to shoot and everything else. That's it.