@Kelrycor
First of all, the hard drive that you linked is the right one. On the package it says that it is compatible for both Xbox One and Xbox 360.
Furthermore, I tried to reproduce the steps in the German manual but unfortunately it didn't work. The hard drive still gets recognized as a USB memory stick. I did not get the option to "Configure Now" but I still got the option "Format" on the Xbox.
Thank you for all the help! I guess the only thing that is left now is to contact whatever Customer Service I can.