Some progress today:
The local dealer, although not certified for this vehicle, was able to help me and he requested a VCI code in order to be able to reflash the BCCM module
The VCI form did not seem to be meant for this, but mostly for retrofits or other module tasks like installing a used one
They had to select "other" and write down the request by hand
Hopefully they will get a VCI code from GM soon and we can solve it. They told me it takes 1-2 days for the VCI code to arrive
I'm glad that we are making progress but at the same time it's so silly that even the dealer must ask "GM, please let me reprogram this module, pretty please?"