Hi, Scott Mindeaux
Good day.
Thank you for posting to the Microsoft Community. We are glad to assist you.
According to your description, I'm sorry to hear that you're experiencing issues with screen sharing in Microsoft Teams on your Mac. Based on the information you've provided; it seems like the issue might be related to the permissions for screen recording on your Mac.
To narrow down this issue, would you please follow these steps and see if it can make any differences:
- Open System Preferences on your Mac.
- Click on Security & Privacy.
- Click on the Privacy tab.
- Scroll down and click on Screen Recording.
- Make sure that Microsoft Teams is checked.
- If it's not checked, click on the lock icon in the bottom left corner and enter your admin password to make changes.
- Check the box next to Microsoft Teams.
- Close System Preferences and try screen sharing in Teams again.
If the issue persists, please try restarting your Mac and then try screen sharing again.
In addition, according to your words: 
Thus, could you please capture the detailed prompted error, and we can explore other troubleshooting steps.
Thanks for your precious time and your understanding would be highly appreciated.
Hope you all the best!
Microsoft Community Moderator.