When hiding a child popup first the app receives ApplicationDeactivate
event and in a short time (a couple of ms) ApplicationActivate.
But the first event hides all popups, so the parent popup gets closed too.
Delay handling of ApplicationDeactivate event in this specific case.
In case of StaysOnTop windows it looks like it is floating already.
But in case of manually setting floating here it has a strange bug
with non-activatable always on top tool window (picture-in-picture).
When first time shown it doesn't act as a stays-on-top window, if you
click on another app it is shown above the PiP. Only if you activate
the main window once more the PiP will become stays-on-top window.
This way it works from the first show.
