Grab the battle.net installer from the lutris website, optionally extend it with the D4 installer (it just creates a second shortcut using the same battle.net install you just did).
Once bnet is installed, you can add Lutris games as shortcuts in steam (you may need to do it from desktop mode without steam running) by right clicking on games and clicking add to steam.
From there you just need to install D4 in the bnet client and away you go.
I used this guide for Diablo 4 recently. Had a small issue where I had to start steam from desktop mode once and maximize battle.net. After that, there were no issues starting it from the gaming mode.
It might look too long at first, but it's really simple. I did it with the SD card part as well and it worked (almost) flawlessly. The only problem I encountered was first launch of battle.net in game mode - nothing would happen, loading was taking forever. I then tried it in desktop mode and the game ran. Went back to game mode and since then everything works without any hiccups.
I am gonna buy it and I've used Bottles to set up the Blizzard game launcher. I already use it to play Overwatch so I'll just install Diablo the same way.