Ubisoft Connect (Uplay) is not installed by default

Since steam does not run UplayInstaller.exe, you need to run it manually. First install the game using Steam. Set "Enable Steam Play for all other titles" in steam settings. Run game once - it will fail, because Ubisoft Connect is not installed. Then install Ubisoft Connect using following command line.

STEAM_COMPAT_DATA_PATH=~/.local/share/Steam/steamapps/compatdata/965320/ ~/.steam/steam/steamapps/common/Proton\ -\ Experimental/proton run  ~/.local/share/Steam/steamapps/common/The\ Settlers\ 7\ -\ History\ Edition/Data/Support/UplayInstaller.exe/UplayInstaller.exe

Runs proton (which is installed in steamapps/common/_ if you have enabled Steam Play). Sets for the run environmental variable STEAM_COMPAT_DATA_PATH to directory same as the game uses. This will install Ubisoft Connect.

You do not need to run Uplay manually. Steam will find it once installed and run automatically every time you run the game from Steam.