How do I repair drywall holes around outlets near my counter?
Cut a rectangle of new drywall that's of substantial size and appropriate for the area to be repaired. I would cover all those screw holes since they're probably weakened behind. Cut out for the outlet box.
Trace the patch on the wall with it in its intended position.
Cut out the existing drywall on the trace using a keyhole saw and/or utility knife. Be careful to not damage wiring.
Float some plywood or scrap lumber behind the cut edge and screw it through the existing drywall.
Screw the patch in place.
Tape the repair joints.

Be aware of where your studs are and either cut down the center or leave some overhang so you can mount the repair backing. Don't cut right against the edge of a stud and don't cut right against the upper molding. Leave at least a good inch.