Can't move or scale circle when adding face

To narrow things down, try these steps:

• Restart the computer (of course, you've done this)
• Re-start in Safe Mode. This bypasses certain potentially disruptive processes, and it often helps. Safe Mode is different for different computers, so see this: 

           Start up your Mac in safe mode - Apple Support 

Those are the easiest things to try first. Then try these:

• Use another library if you have one, or make a small test Library with a few pictures in it and see if the same thing happens. You can create a new Library by closing Photos and then option-clicking on the Photos icon.
• Make a new user and see if the same problem recurs with it
• Rebuild your Photos Library--close Photos and re-launch by option-command-clicking the app icon.

The idea is to find out if the problem is with the Library, with your account, or with caches and login items, and stuff like that. One of these steps may fix the problem, but their failure to work also helps figure out what's happening.

Let us know what happens…

Though you don't tell us, I'm guessing that you're talking about a Mac, not an iPhone or iPad? Which OSs are you talking about.

On a Mac, the one problem we sometimes have (though completely unrelated to the SARS-CoV-2 virus) is that the circle refuses to move, because Photos thinks you're still in the info window and wants to drag the picture there, or something like that. In that case you need to tap on the picture to let Photos know you mean "on the picture," and then you can move the circle. Or, you can just type the name first, and then move the circle.

Does this work for you?

If your Photos Library dates back to 2006, it may contain older videos and image files in a legacy format, that are no longer supported by the current system version. Have you checked the older media in your library for compatibility, when you upgraded from maOS 10.14 Mojave to macOS 10.15? Such legacy items can cause Photos or its background processes to hang and need converting to another format.

Levente Orban wrote: … multiple other circles were revealed underneath.

Ha! Happens to me, too. I've clicked to get a circle, can't move it, clicked again, and again, and when I finally get the focus back to the picture I find it made a circle every time. Never with Steve Jobs, though. It happens most when there's already a face circle there, so I don't see a new one form.

You may also want to close the Info, then open it again.

If all fails, restart Photos, and if it still not suffices, restart the Mac. Then it usually will work again for some time.