TLDR: Try disabling time machine back ups. After dealing with this problem for a very long time, I had given up on it. iCloud just always seemed to get stuck. I decided to try to fix it by doing a clean reinstall of the OS (Monterey). But that didn't fix it. Finally, I noticed that the syncing with iCloud Drive did was blocked by a time machine backup process to an external hard drive. Once I disabled time machine (and ejected external hard drive for good measure), the sync started working perfectly.

I forgot to mention that this is with Universal Control.