Hello,
just a note in case someone has the same problem:
Ubisoft Connect seems to have problems with an update (Regardless of OS, even on Windows where you can just reinstall it), it didn’t work for me in Lutris, and I couldn’t find a solution either. It just stopped connecting.
I solved the problem by launching a game via Steam that uses the Ubisoft launcher. Steam automatically updated the Ubisoft Launcher and everything worked again independently of Steam.