So, i tried both:
I was able to connect the app by removing the buds from the case like described here: Losing connection between left and right earbud - #5 by joram
However, not sure if this is really the reason or it just worked “accidentally” like it did before from time to time.
The problem is, that the update stil doesnt work. it just stays at 0% and doesn’t do anything. I have it open since 10 minutes already, and still at 0%.