I have not had this problem, on either my former '22 C 400 GT (5,000+ miles) or on my current '23 C 400 GT (6,000+ miles). Nor have I read about this problem in the 2+ years I've been reading the forum.
That said, I wonder if some wire providing power to that glove box got disconnected. There's a plug right in back of that compartment -- here's a page from the shop manual:
Also, when that wire-pair makes its way over to the right side, I'm not sure whether it plugs into the wire loom over on the right, or whether it is simply part of the factory loom (i.e., without a plug). If it does plug in, it might be one of the connectors shown in this photo that I took a couple of years ago, when I was tapping into the wires on the right side:
(That's a pic from my C 400 GT gallery -- this particular image and caption:
https://billanddot.com/C400GT/#S-21 .)
Removing the side panels on each side, in order to take a look, can be done in less than an hour, as I did this a few times on each of my two GTs. It just involves removing a bunch of T25 screws and pieces with half a dozen or so metal spring clips on each side, and working methodically along each piece. I mostly use a set of nylon trim-removal bars from a USA store (
https://www.harborfreight.com/nylon-pry-bar-installer-kit-4-piece-63594.html ) and occasionally a trim bar from Wunderlich (
https://www.wunderlichamerica.com/Plastic_Combination_Wedge_Workshop_Tools) to do this sort of work.
If it's not an electrical connection problem -- for instance, if it's a physical problem with the latching mechanism itself -- then I got nuthin', no suggestions, except maybe a brute force attack, and then replace the mutilated door (which looks easy, once it's opened).
Good luck.