Have had the same problem with Google Meet which has been asking to be granted permissions. Have my browser Chrome enabled already in System Preferences->Security & Privacy->Privacy->Screen Recording. But it still doesn't work.
SOLUTION:
I was quite surprised to hear from others in this thread that other running apps might be the problem. So I started quitting them one by one, and checking in between if screen sharing (in Google meet) would work.
Closed Excel. Nope.
Closed Powerpoint. Nope.
Closed Photos - TADA!
For me, it seems the Photos app (yes, by Apple) was creating the problem. Far fetched, but yes...
Note: MacOs Catalina 10.15 on a Macbook Pro, Latest version of Chrome