The drywall needs repair, then taped and spackled. Without tape the cuts will reappear almost instantly.

I would use joint compound and some tape over any areas where it's ripped/broken.

If what I'm seeing is rough edge between multiple coats of paint and unpainted drywall sandpaper and spackle should be ok. I would remove trim from new light while doing it.

The quick and dirty method would be to use ceiling fan trim to cover it up.

Thank you all for your help.

What I'm grappling with is under "typical" circumstances, you can replace drywall by "enlarging" the hole with a cutout. Even if that were possible here, I still think the process is beyond my own skill level. But in any case, this is a recently installed recessed light - I can't cut it out. So how can I repair the spot at around 11 o'clock that is cut?

And yes, klem1, the circle you are seeing is a rough edge between multiple coats of paint and unpainted drywall EXCEPT for that spot at around 11 o'clock or so where the drywall is torn.

" So how can I repair the spot at around 11 o'clock that is cut? "

Tape and spackle. Remove anything loose, spackle, tape and spackle with sanding. Prime and paint. Or buy the mesh fibatape (self-stick) and skip the first layer of spackle.