I was hoping there would be some fix for the performance issues that plague W:UM on newer hardware/operating systems (low fps, stuttering) but alas, it still happens.

Did you disable anti analysing. Tried window mode
Or used the Special K mod on this game. I really don't have performance issues for now on my laptop pc which is probably around the era that the games came out.
Also check pcgamingwiki don't know if the anniversary patch can be used on gog version
I noticed a user named Heatray posted this on steam:
I have a Radeon RX5700 XT and with standard settings the game produces ~40 fps
after trying different settings, the game began to produce 60 fps with vertical sync enabled and only in windowed mode
it is not very convenient to play in the window, I found another way

you need to download the Special K mod
https://discourse.differentk.fyi/t/download-special-k/1461
copy SpecialK32.dll from archive to the game folder and rename it to OpenGL32.dll
start the game, press control+shift+backspace and turn on frame limit

I encountered the same problem in Worms 3D, Worms Forts & Worms 4 Mayhem and it was solved with Special K

Mine is weird to say the least, I'm running it on a 6700 XT and a 170 Hz display at 1440p and the framerate is quite bad, to the point where I can't even scroll through the menus properly.

It seems to depend largely on the refresh rate setting in the launcher, however neither option works well and neither makes any sense...

- If I set it to 170 Hz I get around 60 - 70 FPS but it's super choppy, bordering on unplayable.
- If I set it to 60 Hz I get 170 FPS but it doesn't feel like it, it feels closer to 40 - 50 -ish FPS at most.
- Windowed/Fullscreen and Anti-Aliasing have no effect on performance.

Mind you I'm relying solely on the Galaxy framerate counter since Radeon Software doesn't seem to work with this game at all. I'm not running the latest driver but that shouldn't be an issue seeing as the oldest driver available for this card came out a few years after the game.

Use the performance fix, it's on pcgw, search on google "worms ultimate mayhem pcgw", i had 60 fps before using the fix, but every 4 or 5 second, fps would drop to 40 -50 fps then back again to 60 fps, after using the fix i had 70 - 100 fps and it never dip under 60 fps with Ryzen 5 1600 and RX 570 4GB and a settings like these.

Resolution : 3440 x 1440
Shadow Resolution : 4096
Anti Aliasing : Off
Refresh Rate :144 hz

I am pretty sure it causes mouse issues.

Try with RivaTuner Statistics Server, it will works 100% for both WUM & W4M whet you set value of 60 to Frametime Limit and Scanline Sync. I found this solution because recently I go with AMD and they drivers doesn't have Fast V-Sync option like NVIDIA who can unlock the FPS WUM & W4M.

V-sync cannot unlimit FPS. Its made to limit it. It cna increase limit though, higher than its supposed to be.
So V-sync/*-sync are obsolete. FPS shouldn't relied on display refreshrate in the first place... Kinda relied... Whatever.

As for NV and mine experience - using 3rd party tools work better than bugged NV control panel(/whole driver's). Limit FPS manually is alway safer way to make games work properly. Driver panel or 3rd party tool, if there is no in-game option to limit it.