@Boris
MIDI is one way to control the mixer core. The others being the surface (touchscreen/faders/rotaries/keys) and any remote apps (Qu-Pad, Qu-You, Qu-Control).
When the mixer core is updated, changes are sent out to all of these control types so they’re displaying the current mixer settings.
The current screen you’re viewing on any of the connected devices does not make any changes to the mixer core, and similarly scene changes do not change the screen being viewed (though maybe the settings being shown on that screen).
So no, there is no way to use MIDI control to change the screen being shown on the Qu itself.
Hope this all makes sense!
Keith.