A little off topic, but we have a couple of things which might be helpful for the ‘global’ portion of your request. If you enable the display local time in user card site setting, then everyone will get their local time displayed on their user card. For example, on our internal instance, my user card looks like this:
We also use this theme component to help visualize timezone overlaps:
Admittedly, neither of these let people define their own ‘working hours’, so they don’t solve the day/evening part of your suggestion.