What could explain a large hole above water heater vent pipe?
It looks pretty obvious to me. Whoever installed the water heater vent intentionally scored the drywall to make a hole for the vent to pass through. I can see the square cut made by a utility knife and they used a hammer to break out the drywall. Then whoever installed the vent did not finish the job by repairing the drywall keeping proper clearances etc.  It is just a sloppy job.