OK, the iOS version info was important. I can reproduce the issue on iOS15. I don't know yet what is causing it. The testflight version did run on iOS15 fine. I will have to investigate and try to fix it in update 1.0.2.
But out of curiosity: why do you stick on this really old version of iOS if your device is able to run the latest iOS version? And even within iOS15 you are on the old 15.7. The current iOS15 version is 15.8.4!
So if you can update, I would recommend to update iOS. All versions starting with iOS16 work fine with the external screen setup (just checked 16, 17 and 18).