The NCDC (like any double DIN unit) do stick in their cages a little, making them challenging to get out. Good quality extraction keys help, ie not the Autoleads and similar ones. Some members have made a hook to grab the main chassis of the unit through the CD changer slot, but unless you've seen one apart, its impossible to describe where to hook onto, and most likely you'll end up hooking the actual CD Changer, or worse still, the front panel.
Under no circumstances pull on the front panel, it will easily break.
With good keys, you should feel them latch on, and as you pull the keys apart, should be very hard to pull the keys out. So with the keys latched on, pull them apart and outwards, but also try to shake them a bit, to wiggle the unit slightly in its cage to break the sticktion.
When you eventually get it out, before refitting, give it a wipe over with a silicone spray and spray inside the cage, the sort of thing used on plastic ccurtain rails, like
https://www.amazon.co.uk/WD40D-N-A-WD-40-Silicone/dp/B006UCNI38/ref=sr_1_5?adgrpid=56958497447&dchild=1&gclid=Cj0KCQjwppSEBhCGARIsANIs4p5Fl78_enTnJdwwU0vy6NRhzlEcUvenhh0Vbih5puD3AuLQHl4S4IMaAjFKEALw_wcB&hvadid=259024407336&hvdev=c&hvlocphy=1006551&hvnetw=g&hvqmt=e&hvrand=1661154562396996356&hvtargid=kwd-314187370201&hydadcr=28154_1724864&keywords=wd40+silicone+spray&qid=1619364389&sr=8-5Obviously, avoid getting on the connectors or the facia.
As for why Opel are having such difficulty, I can't comment. Here in the UK, Vauxhall dealer technicians are usually working at a franchised dealership because they can't get a job anywhere else. That, added to the relative rarity of the Omega makes dealers useless here for Omegas.
As the screen is completely blank, as if its not getting power, I assume you have already checked on the fuses? If not, the display use powered through:
Fuse 2 (15A)
Fuse 15 (20A)
Fuse 12 (20A) << Also powers the NCDC