How do I Reauthorize Screen Sharing for Quicktime?

You can reset the screen recording permissions for QuickTime Player using tccutil:

tccutil reset ScreenCapture com.apple.QuickTimePlayerX

After running this command, you need to quit QuickTime Player (if it was open). Then open QuickTime Player again and choose "New Screen Recording..." from the File menu. That will cause the prompt dialog to pop up again so you can grant permission for Screen Recording.

Quitting and restarting Quicktime several times seems to have made it a selectable option in System Preferences. Once it was selected/checked I was able to perform a screen recording with Quicktime.

Running a tccutil reset command did not help me. No apps appeared in the Screen Recording list, as shown in the screen shot of the original poster, and I couldn't figure out how to add them back.

Nic, who posted about a similar situation, suggested that I create a new login user account and log in there, and then get QuickTime Player to record the screen in the new account. This worked for me. Here's what I did:

Starting in my main user account, I created a User 2 account with admin privileges and then switched accounts. In the new account, I launched QuickTime as well as a couple other relevant apps (screen shot and screen sharing apps). Each time I did that, I got the usual prompts to allow Screen Recording access and those apps finally appeared in the list so that I could check them.

When I finally switched back to my regular user account, those permissions were retained, so that I could finally run QuickTime and make screen recordings.

Hope this works for you too.