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As a drywall painting contractor I think that would be too small to even cut and patch or brace for that matter.
Just use some lightweight patching compound ( I prefer hot mud or premixed spackle ) and just float it, sand when dry and you should be fine.
Alot of it will be covered by the plate as well.
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That should be less than 2 hours to cut out square, install a small wood brace anchored to drywall on each side.
Put in a small piece of the same thickness drywall.
Mesh tape, Easy Sand20 Lightweight.
If you are good at drywall you should be able to strike that smooth with single coat.
Remember you can put another coat on Easy Sand as soon as it is set up.
You do not have to wait for it to dry, just set.
It actually bonds better to the still damp fist coat.
Let set overnight, touch up paint, done.
That is such a small area getting it flat, level, and smooth with knives will be easy.
Use a knife wider than the area and make careful stroke down from the box.
You may have to pull the switches out on their wires to get a drywall knife under the support tabs.