I've been playing online FPSs for years now, but I've always been absolutely terrible at them. I can maybe get a 1:1 K:D ratio on a good round, but my average is probably closer to 1:3 or 1:4. This has been pretty consistent in every FPS I've played over the years. I'm not sure what I'm really doing wrong. I use cover. I try to flank with my teammates. I throw grenades to flush enemies out of cover. But somehow it always seems like they're faster, more accurate, better able to get the drop on me.
Is it just because I only play them for a few weeks or months before moving on? Is this something that gets better with practice, or do I have some kind of undiagnosed motor deficiency?
It's pretty decent for drills. Being able to do different types of drills is important too, for example in Overwatch the majority of characters require you to have tracking skills rather than twitch-aim skills, Quake on the other hand is about snapping to very fast moving targets, and Valorant/CSGO are about crosshair placement and understanding how corners are cut and where people hold corners on each map. Different types of fps games have pretty different skills that require fairly different techniques. Crosshair placement is a universal one that you'll find valuable across all of them though.
Gamesense is the hardest of all of them to learn, it's one you only get with in-game practice over and over and over and builds up over several hundred hours in a game really. You learn to feel the flow of maps, and know the general distances that enemies can cover from their spawn to possible locations that you'll encounter them so you learn to know when you're going to see the enemy before you've even seen them.
Another one here is headphones audio too, use headphones, positional audio information is a significant advantage you can not get from speakers.
For reference I use a 1200 dpi mouse with 5.55 sens in Overwatch which is 8.190008 inches/360 according to this. I don't know what you use, but this works for me, probably a little higher than some others are suggesting here. I would probably go lower if I had more space but my desktop space is limited. Anyway I'm not amazing or anything but can definitely confidently be above average at most.