When the android back button is pressed to remove the keyboard, the Qt.inputMethod.visible flag is still true.
This only happens when the input TextField has no predictive text active. It is not possible to clear the flag by hiding the keyboard programatically, using Qt.inputMethod.hide(). This does nothing.
When the back button is pressed again, the visible flag is cleared. This "eats" the back button press as well, so the app does not respond to it.

I have attached a small project that exposes this behavior.

The app has been tested on an android 11 Google Nexus 4, but the bug has been reported on numerous android 11 devices by our users. Including Oneplus and Samsung devices.
The Nexus phone uses the standard GBoard keyboard.