I have made pita twice recently, both times it stayed puffed after baking. I know when I have bought it from the store it was flat.
It tastes great, it is just difficult to store.
Yeah, I'll echo the lack of holes being the issue. If you check commercially made pita, there's perforations. You might also wanna dial back the temp a tad to reduce crisping
That being said, puffy pitas are perfectly normal. They tend to be softer though