I figured it out.

I added the Ubisoft Connect installer as a non Steam game, installed it with GE-Proton9-4, and then switched the shortcut to the location of “UbisoftConnect.exe”.

Then, in the launch options, I put:

PROTON_BATTLEYE_RUNTIME="$HOME/.steam/steam/steamapps/common/Proton BattlEye Runtime" %command% uplay://launch/15657

And make sure the Proton BattlEye runtime is installed through Steam.

I played multiple full matches in a row like this without any issues.

Edit: Oh I almost forgot, you also need to get a copy of pdh.dll and put it in the game’s directory.