I have flown in and out of GPT countless times when I lived in Florida--WITH my cat!! But now I live in Ocean Springs which is a good thing because I refuse to get on a plane when I have to muzzle myself. GPT is one of tiny airports that are quite user friendly, however from time to time you get tied up because of military trainer planes utilizing the runways.
The ones I’ve visited have always been super clean! I believe I can recall one family restroom downstairs near baggage claim but I wasn’t on the lookout for those so there very well could be more!