This is my understanding as well; if the PO owns the land, the parking lot is a prohibited area. Otherwise (strip mall) it’s just the Post Office building itself.
I had to get an accident report at my local PD records office the other day. I thought about this topic there as well. Not going inside with a firearm obviously but I wondered if the ‘no guns in the parking lot’ rule applied. I’ll have to go find out what my local LEO guidelines are for this.