Installed Battle.net client, D3, WoW, and Hearthstone on a brand new Mac Mini running macOS Big Sur. It’s the latest model with the M1 chip.
WarCraft and Hearthstone both run (and remarkably well), but Diablo 3 fails to launch. The splash logo appears, but then it throws an error “Application Initialization Failure. Diablo III was unable to initialize.”
I’ve tried uninstalling the game, deleting it from Applications, and then having the client re-download it, but I still get the same behavior. 
FIXED. UPDATE:
After following some helpful guidance from Blizz support (adjusting folder permissions, removing bnet client cache folders, repairing the game) that unfortunately didn’t resolve the problem, I completely removed the bnet client and rebooted.
After booting back up and reinstalling the bnet desktop client, I was prompted to install Rosetta again. I don’t know why that came up again, but I went ahead and confirmed the prompt to install Rosetta again. Afterward, I ran the bnet client and was able to launch Diablo 3 without issues.
Not sure why WoW and Hearthstone were unaffected, but hey, everything’s working now, so I’m happy. =)