[Zubersoft]

I tested on my Samsung S8 Ultra and it behaved as I described. I tested with every combination:

Dim the navigation bar off, hide the navigation bar off, fullscreen off
Dim the navigation bar on, hide the navigation bar off, fullscreen off
Dim the navigation bar off, hide the navigation bar on, fullscreen off
Dim the navigation bar off, hide the navigation bar off, fullscreen on
Dim the navigation bar on, hide the navigation bar off, fullscreen on
Dim the navigation bar on, hide the navigation bar on, fullscreen off
Dim the navigation bar off, hide the navigation bar on, fullscreen on
Dim the navigation bar on, hide the navigation bar on, fullscreen on

and it seemed to work for me as expected with each. The status bar would always automatically fade out when fullscreen mode was on, otherwise it would stay on if fullscreen mode was off, and I never saw it overlap with the action bar or tabs on the library screen. So I'm not sure if what you are seeing is an Android 12 vs 13 issue or something else. I can keep looking into this, but I'll need to figure out how to reproduce what you are describing.

Mike