I know this "solution" may sound totally bananas...but it worked once...
User running MacOS Catalina 10.15.7
Running latest build of MS Teams 1.3.00.26266
Unable to use Screenshare
I remoted into her mac with TeamViewer
Started a Teams meeting between her and I
On her mac I attempted to start Screen Share
System prompted to enable in System Preferences
Clicked the OPEN SYSTEM PREFERENCES button and MIRACULOUSLY the MS Teams options was now available in Screen Recording.
Sounds crazy...but worked.
What's even crazier...I am running exact same make/model of MacBookPro, exact same MacOS, and exact same build of MS Teams and have not ever had any issues!
Good luck all!