In vanilla multiplayer Minecraft, although mobcap is dependent on the number of players, spawning will still be done per server. This means that some players/locations will take a very big percentage of the mobcap, while others almost won't have any mobs, making mob farms very unreliable.

PaperMC solved this by introducing per-player-mob-spawns which will make that mob spawning will be counted per-player (more detailed explanation by PaperMC developer on Reddit, PaperMC patch source code that implements this).

Is it possible to implement something like this in Carpet (or carpet-extra)? This would be very helpful for people who use Fabric on their server and need mods, as I wasn't able to find any updated existing mod with similar functionality.

But that messes with how mobcaps is itself calculated, which unlike most people think is not by the amount of players online but actually the number of chunks loaded.

you can't find a mod with that for a reason - it messes up with fundamentals of mob spawning. If you want that feature from paper - you probably need to run it on paper.