Thanks for the fast reply and the welcome!

The booking was made on a third-party site (flugladen.de) and it appeared as BA for the outgoing flight from Berlin to Mexico (with BA numbers for all 3 legs) and AA for the return flight (same route MEX-DFW-LHR-BER, AA flight numbers). So I assumed BA was the "main" airline" at least for the outgoing flight and indeed the one which operates my first flight.
I have tried to add the suitcase on the AA website but got the same result - they don't allow the purchase of baggage items as a part of the trip is operated by another airline. Seems logical, but I would assume code-sharing partners have some sort of coordinated policies to make this easier...

I am trying to get the eticket receipt at AA but there is an error message. The only additional info I could find is this:
/C1*3-4 NONREFUNDABLE RESTRICTIONS APPLY /C5-7 VALID AA/BA/IB/AY-NON ENDOCHG FEE APPLY/NO TRANS