Sorry to be insistent, but BERUF is the word used in my German A1 book... and I would argue there were some professions (most of them unusual, I grant you that) which weren't a craft, in the sense of making something with your hands: politician, priest, vestal virgin, taster, accountant, author...
Do you still disagree?
I think my translation "what is your occupation" should be accepted. Occupation is more general, and includes professionals. How many applications ask what your profession is...it's always "what is your occupation". A doctor or a wrestler could both call themselves professionals? why so picky?