Photos won't ID People anymore

Kris - are you using "Optimise Storage" with iCloud? Photos needs the original versions, so make sure, that they get downloaded from iCloud. View the photos and videos enlarged, also try to add at least one face manually of a person you want to get named.

"Not using the app" means that Photos should be running in the background. Keep photos running, but not as the frontmost window.

If you just upgraded from an older system version, ensure, that you do not have legacy media in your Photos Library, that Photos 5 on Catalina or Photos 6 on Big Sur can no longer process. Older videos in a legacy format may be blocking the face detection, also PDF files or other unsupported image formats.

How to Weed out Legacy Media in Photos for Mac - Apple Community

I had the same problem with a local library (quit Photos or left it to the background, did not touch the mouse etc -- no matter what 0 faces). But after just sitting there for more than a month, Big Sur Photos.app finally started to add faces two weeks ago! It seems to prioritize Memories because it also slowly adds them before adding more faces (380 GB Photos library with 37 000 images or movies in an internal Mac mini 2018 SSD at ~/Pictures). In Mojave this process took "only" a few days or up to a week for basically the same photos and movies in a library also created from scratch when Photos randomly decided to do that.

I have a hunch that the face recognition best wakes up if I happen to shutdown the Mac and do a cold boot, then open and quit Photos.app and maybe log in to gmail or Apple forums (don't know if all that is necessary...) and then go Finder > toolbar > user account icon > Login Window... and leave it at that for a while (I otherwise seldomly do that). With that workflow yesterday all faces were finally done.

It took more than a month on my Mac as well after the Big Sur upgrade, Matti. And that for a moderately sized library of just 50000 items. I suspect the face detection has been paused while my Mac has been connected to power, but has been showing "Charging on Hold". When that happened, the Photos.app has not been showing as using significant energy, as it should have been using. The face detection has made more progress, after I disabled "Manage Battery Longevity" in the System preferences > Battery, but as I wanted to protect the battery I turned it on again after a day. It is not a good idea to turn it off, but I wanted to know, if it makes a difference.