The fullscreen support for iPad is enabled (white-listed) for iOS 13.4 and higher now.
Actually it is activated also with 13.3.1 However it works very bad.
I just bought a new iPad Air which came with 13.3.1 and fullscreen button was activated. The problem was that zooming did not work.
It kind of jumped back when you zoomed in.
After updating to 13.5.1 it works.
While in 13.3.1 I did some testing an found also this weird bug. Tapping on the image gave me this popup. I have not been able to reproduce it in 13.5
It is actually a Zoom image which is opened fullscreen from a popup
https://www.360-foto.dk/fullscreen-bug.jpg