sort on people in photos app

The library size should not be a problem with only 13000 photos.

"I'm using OS 11.6.5 on a MacBook Air and my computer will no longer sort photos using facial recognition as intended. It was working some time ago, then got stuck"

What do you mean by "got stuck"? Is there a message below the People album? If yes, which message? Can you identify a photo, where Photos should have detected a face, but did not find any? As a test, enable the option to show the faces names on all photos in the"View" menu, so you can see easily, where Photos stopped to scan for faces.

In addition to restarting the photosanalysd as described by muguy, you may want to check, if there is a problem with your Photos Library.

Common reasons for Photos not being able to complete the the scan for faces are:

• lack of storage: check, if you are still having plenty of free storage (at least 10GB) on your Mac and in iCloud, if you are using iCloud Photos.
• Legacy media, that can no longer be processed in your Photos Library - I single video, photo, or Live Photo that can no longer be processed on macOS 10.15 Catalina or newer can block the analysis of the photos.
• Problems with the filenames, permissions, or file ownership or a damaged Photos Library: If you are not keeping the Photos Library in your Pictures folder, check, if your Photos Library is on a compatible volume, as described here: Move your Photos library to save space on your Mac - Apple Support

Try this:

Quit Photos App

Open Activity Monitor

Click "process name" to sort alphabetically

Select photoanalysisd

Quit the process (look for the x in the octagon)

Restart your computer

Open Photos

That should kick off the photo analysis process again. It may take some time to begin processing facial matches again.