Just an observation. I had this two and half years ago with my 2011 Audi (wash my mouth out) A4 S-Line Avant, the precursor to my GLA 45.
The Audi was missing its Sat Nav disk and the selling dealership agreed to supply me with one. They purchased one on eBay (for about £30) and we slotted it in the car. Nothing....
After a lot of investigation and phone calls (all which was as new to the supplying non Audi franchised dealer as it was to me) it transpired that the Audi would not only NOT read a copied disk (anti piracy software built in). But it needed a genuine Audi disk and two hours of Audi labour to reprogram the navigation system. I am still none the wiser how they did all that or why it took two hours to flash a disk or the like! I can tell you that it cost around about £300 all in of which the dealer I purchased it from coughed up the cost. Very decent of them, but only fair.
To be honest sky high prices don’t surprise me, but if I were you I’d try several dealerships just to be sure.
To end on a plus, ten years ago I first stepped into Mercedes ownership with a 2004 C180K estate. Three months into ownership some oik ripped the bonnet star from the front. I drove over to the local dealership and prepared to shed a lot of tears and cash. I said “go on surprise me”. They did - £25! They said would you like us to fit it? How much? I said. Free, Gratis.
For the next six years that dealership got all my trade. So there was a happy ending.
Good luck with your search.