How can I repair a circular drywall patch seam?
That electrician was no plasterer.

First you need to get rid of the high spots where the paper part of the drywall is showing through, you might need to cut that out with a knife. after that you just need to fill it with plaster filler until it's flat then sand it smooth and paint.

If you light it at an extreme angle the high spots will be easily visible.

you probsbly want to use poweder based fiiller, not pre mixed joint compound,  the powder stuff sets hard quicker and shrinks less.