Lol. Not even slightly.
If a post office is in a strip mall, as many of them are, then the parking lot is the strip mall owner's property. If the post office is a bank annex, as it is in my town, then the parking lot is the bank's property.
If it's a freestanding PO, then MAYBE the parking lot is "federal property." It's just as likely to be owned by the town, or by a developer. It's likely that the loading dock and the driveway leading to it are "federal property," but it's not like you're parking there.
Who cares? I'm another one who doesn't bother disarming when going to the PO. Hypothetically. I mean, anyone truly worried about getting nicked by the feds for leaving a pistol in the car of a parking lot is not being sensical.