So sorry to hear of the issues with your AirPods Max, Tobias. I have not had any issues with my Maxes but it sure sounds like a logic board issue. How comfortable are you with attempting to repair them yourself? According to iFixit, the right ear cup houses both batteries along with the main electronics / logic board so it might be worth following their guide and taking a look.

https://www.ifixit.com/Teardown/AirPods+Max+Teardown/139369

I totally agree that this was not an update but also relieved to know that my headphones are current for at least another year, maybe.