Thanks everyone for the replies, the problem was that I had installed the beta on an external SSD. Apple Intelligence only works on an internal hard drive, so I have now installed the beta on another APFS volume and it works.

it looks like it is not available in the EU again :(

It may sound strange, but I was able to fix it by logging into the AppStore on my old iPad Air with iOS 12 and then renewing my membership there. I don't have Apple Pay on there, so it was possible to use PayPal.

Same Problem here, its not Possible on AppStore Subscriptions and also not possible on the developer app, the developer app says "Valid trough jan 8, 2024" but we have 14.Jan.