What does it mean Slack is active green dot but with a Z, and how to change it?
Solution 1:
This comes from the "Notification schedule" setting in the Notifications menu in Slack Preferences.
Basically, this sets your "working" hours. Outside of these hours, the "Z" will appear to show that you are outside of working hours and your notifications are turned off.
To change this:
Slack -> Preferences -> Notifications -> Notification schedule
To change it completely, change it to Everyday from 00:00 to Midnight.