Finally it worked. Deleted all cookies in Safari on my iPhone (again), started the configuration from scratch and payed with my Visa debit card. Authentification poped up and worked, I could see the 2050€ debited to my bank account in the bank app. Then … the error message from the configurator poped up. Frustration, I checked my emails and found a mail from Ineos with the confirmation of my order. Now I should be happy, but I am still pretty much frustrated about this hazzle.