After updating to 13.4.1, it's finally fixed for me as well!
Only took 8 months, but better than waiting for macOS 14. Still boggles me how this slipped in and took so long to fix though..
Ironically I never found out when macOS clears the icon cache, I suppose it wouldn't have mattered in this case though. But it seems to be after updating and a reboot? Although I restarted once or twice on 13.4 and didn't see any difference.