When I have these sort of mixed BA/AA bookings, I may have either 2 or 3 PNRs. I’ll always have a master BA one (assuming BA booked). If all the AA operated flights are prime flights, then I’ll only have one AA PNR. If there’s a mix of code shares and prime flights, then I’ll have 2 AA PNRs. In the AA app, the main AA one will have all segments in the whole itinerary, but I’ll only be able to select seats (and I think check in) for the AA prime flights. The other AA PNR will have the BA codeshares plus the BA prime flights for that direction; and I’ll only be able to change seats and check in for the BA codeshares via that PNR.

I usually find it easier to book AA prime flights from the start. But with schedule changes BA agents try to book BA codes but on some sectors there isn’t a codeshare.

As others have said, it’s nothing to worry about and you’ll get all boarding passes you need at the desk if you can’t get them online somehow.