The Post Office isn’t a GA state government facility. It’s Federal. Different rules.
Correct. Ga law doesn’t cover Federal property. You will be violating Federal law and will be prosecuted in Federal court, not state.
It is (or was till last year, didn’t see if it was changed) also illegal to have a firearm anywhere on airport property, including the parking lot. This makes it rather dicey to take your favorite O/U with you on that next Grouse hunt out west.