Seems as if we have been following a flawed process (at least from the consumer end) for years. Maybe we just have to be content with what was once cheap stuff that kind of works. On the other hand, we have some old closed circuit stuff that is still working and even some 10 years old FDT cameras that still work as long as you have a firewall to keep them from being hacked.
Just checked two of mine. BOth were updated to 16 when it came out and to 16.1.1 yesterday. I am seeing no change to the way the app has always worked. As you say, mine go into landscape when selected from the home screen - the home screen which still will not display in lansdscape. When I wish to go back the return carat/arrow whatever it’s called does nothing… until I turn the whole iPad to portrait - then the carat/arrow behaves as expected.
If you are running an iPad that supports Stage Manger, turn on Stage Manger and see my post with instructions above (post# 42).
If not running one of these iPads, then nothing has changed other than the orientation flip button 
is broken in the production app. The bug is that the button flips to an old still image instead of changing screen orientation. The bug is fixed in the current public beta app.
The broken “back” button in landscape appears to have been fixed in at least the latest iOS release…