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.
Which Wine runner are you using?
Every so often, a Battle.net update breaks it in Wine, and a workaround must be found. It takes time for these workarounds to make their way into upstream Wine, but game-focused variants like GE-Proton often pick them up early. I suggest trying the latest GE-Proton Wine runner.