Steam can install and run the blizzard launcher. Add the blizzard-setup.exe using "add a non-steam game to my library". Set the compatibility mode to Proton. On first run, it will launch the blizzard client installation. The next runs will just open the launcher.
I was able to play Overwatch on an AMD ubuntu laptop flawlessly.
I was able to play Overwatch on an AMD ubuntu laptop flawlessly.