Great question — answering as the UphillTech team:
Cut off the loose paint with a razor knife. No sanding is needed. The area looks small and will not need a large area to feather the new compound in. The technique is a bit of an art. Use some general purpose drywall compound and fill the void part of the damage area. It does not have to be perfectly flat, in fact you want a few peaks. If there are no peaks add some by dabbing in compound with a small putty knife or even your fingers. Your want about 5 to 10 peaks to be hanging down like stalagmites from the ceiling about 1/16" to 1/8". Then take a wide drywall knife or if you have it a knockdown knife and gently swipe over the area to smooth down the peaks. this will give the texture and...
Full answer by RMDman: https://diy.stackexchange.com/a/331486 (CC BY-SA 4.0).
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