Do you use an application launcher / configuration manager like Lutris to do this? Or do you mean directly through steam? There's a steam game that I play often that tends to work the most frequently with proton hotfix for reasons unknown to me.
No just directly in Steam. You can just add a non steam game to your library and select the .exe file you want, and steam will create a c drive environment for each non steam game you add.
In some cases you might have to change which exe file it runs, if you initially run a setup.exe which creates the real exe file you'd want to launch inside the c drive environment folder
Yeah, why not? Steam has non games on it by default - mostly art programs and utilities for whatever reason. When you're adding a non steam game to be run through steam it's just a wrapper and shortcut to it.
Yes, Battle.net runs flawlessly in Steam, have zero issues playing D2R and D4 this way. In fact D4 ran flawlessly on Linux on Day 1, which came as a bit of a surprise to me.
Lutris doesn't have to mean Wine. It can launch apps via Proton too (and so can Heroic). I think it uses https://github.com/Open-Wine-Components/umu-launcher behind the scenes, not sure, but so far I haven't run into any issues with this approach.
This is exactly what I do, works great. I may have had to try one or two different recent versions of Proton via the drop-down, but it's way less hassle than when I used Lutris.
I played WoW for several years this way without much issue. The only tweaking I ended up doing manually was to try to figure it out how to get the game to let me enable ray tracing, which I did get working but ended to being too much of a performance hit for my to leave on most of the time anyhow.