Barstool lets me still see the time/date and other useful info while hiding the menubar. I can see wifi connectivity, date, time, and battery all the time.
The app also observes system notifications to surface now playing state, (Apple) calendar events, and volume/brightness changes.
I've had to do a lot of finking with mac PrivateFrameworks as apple loves to make all the interesting data unavailable through official sources/APIs.
Happy to get any feedback/questions!