Questioning how a minimized, modeless child dialog is drawn

The attachment shows how a minimized, modeless child dialog is drawn.

You can easily reproduce this behavior running the qt WIndow Flags example, selecting "Dialog", check marking "Window minimize button", then minimizing the resulting Preview window.

For an app with more than one minimizable, modeless child dialog , the default representation is not acceptable since there is no way to tell one minimized, modeless child dialog from another.

Apparently, setWindowIcon() is not obeyed when a minimized, modeless child dialog window is drawn.

Overriding paintEvent() and doing something different when isMinimized() does not work because apparently the paintEvent() isn't even called under the minimized context.

setMinimumWidth() is not obeyed when drawn minimized.

Could the default drawing of a minimized, child dialog be improved?  Is there a workaround to drawing the minimized state myself?

Somewhat related Windows reference https://docs.microsoft.com/en-us/windows/win32/gdi/drawing-a-minimized-window