I'm so deeply annoyed by this. I own a 1500€ machine and can't even read the time because its greyed out. Can't find a solution either. All in all Big Sur is very buggy. Edit: Big Sur may still be buggy, but this is definitely not a bug, nor a problem. The grey date/time display informs you that the do not disturb mode is turned on. Just uncheck the moon in your control centre.