I’ve looked around a little, and found some mentions of using Lutris, or running it through Steam (tbh I don’t know how that would work), but I’m not really able to find any guide that explains the process well enough. I’m so used to the game being handled by Blizzard’s Battle.net launcher, so I can’t really wrap my head around how that would work.
Lutrius with proton-ge_latest works for me to get battle.net installed and run wow. I use proton-up to install the different proton versions. Then you need to setup lutrius to use them.