Another stupid quirk is USB-C HDMI output sometimes outputs 4:3 mirroring of the iPad screen even when in a full screen video. If you reconnect and fiddle with pausing/playing the content while screen locked, you can “trick” it to use presentation mode at the screens native resolution.

Half the problem is flagship apps like HBO/Netflix don’t implement this correctly.

Oh and this is all different if you have a keyboard attachment because only then are you allowed to “extend” display which can use the screen’s native resolution.