Improved way to control windows state when it comes to foreground.

User has following requirement:

"I would like to create two applications that both run in full screen mode. The first one (red) runs in full screen and launches the second one (green) in full screen then minimizes itself. On exit from the second one the first application (red) restores in full screen."

Depending on macOS from BigSur to Ventura the behavior will change:
"Either the second application (green) does not start in full screen or sometimes comes behind of the first application, or the first application (red) does not restore properly in full screen."

User has been checking the window state change with visibilityChanged signal, to make sure that window going out of full screen before moving to another full screen but this did not help:
"I was able to connect to visibilityChanged() in a subclass of the QWidget and wait for the window state to exit the full screen before entering full screen from the second application. This did not seem to help though. On the way back, the red application seems to stay framed."

Could there be an improvement with parent-child relationship of two GUI processes that the child process can choose its windows state when it comes to foreground (i.e.: full-screen) and preserve the window state of the parent process on return back, in a well-defined manner?

Users example has been attached.