So, it is most likely that the screen and button graphics are CGI images using blue screen, in the show.
On a prop replica, the simplest thing would be to use back lit gels that could easily be changed out.
Since the pop up portion looks to be "bottom" lit acrylic, the ''button graphic'' portion could be back lit using a flat
led panel I showed in a different thread.
This would allow the pop up to have room behind the backlight when pushed in.
If there are more then one prop which are static (no moving parts), then one could be made open all the time
with lighting and animated graphics and the other could just be closed for the Comm usage.
Maybe a third could be a pop-up/no graphics, but with pop up action and reset.
Did someone post that they can get pictures and dimensions from an actual prop(s) used in the episodes?
That would save a lot of effort.
.