Select "Browse"
Choose the "Battle.net-Setup.exe"
Right-Click -> Properties -> Compatibility
At time of writing stable and working Proton version is "Proton 8.0-5"
if that doesn't work or silently crashes at any point, try a different version
You can leave the install location for the Client unchanged, but then the next time you remove the Setup as a non-steam game and re-add it, you lose the installation and have to do it again.
The persistent way is to choose a directory on your computer, not in the emulated windows environment.
To select a directory on your computer click the "Change" button when the Installation asks you to select the Install Location. On the left hand side select the "/" directory and navigate to where you want to install the Client to.
"Select Folder"When the installation is done...
You can safely remove the Setup at this point as a steam game and add the Client .exe as a non-Steam game. Or you can change the location of the Setup-non-steam-game, either is fine.
After you added the Client as a Non-Steam game don't forget to select the Proton version again.
The Install Location for the games should also be on your computer and not be the default, otherwise the same applies and the installation vanishes, when you remove the Client as a non-steam game.
You can change the name of the entry in the properties from "Battle.net.exe" to just "Battle.net" and also set an icon there.
"Set Name and Icon""Logo"You can right-click the empty gray space above the title and "Set Custom Background".
"Set Custom Background""Background"