I recently updated my washer box and am now looking to patch a small area on the stud, which I've highlighted in red. I can see two ways I could do this, one is to cut out a piece for this repair and use mesh tape. Alternatively, I can also use California patch.
I'm fairly new to drywall repairs, is there one method better than the other? Would an all-purpose mud from Home Depot be suitable for this task?

