I have a similar story too. I booked AA codeshare flights through Citi Thankyou. (For some reason, CX was showing Y and PEY was sold out, but AA still showed availability.) I've booked AA codeshares before on AA.com and the drill is to ask AA for the CX record locator and then I would be able to pull up my booking on the CX website and manage my seat.
The website has an error if I use my name/record locator. I appended my middle initial as usual and that didn't help. When I look it up with my ticket number, it says "No RLOC Associated with this ET". If I pull it up on the CX app, I can see the itinerary but I can't make any edits like seat selection. It just says refer to the operating carrier. The booking ref also works in checkmytrip - which lets me see the seat map.
I called CX on Sat and they confirmed the booking reference that AA gave me was correct and let me select seats. They had no idea why the website didn't work for me and sent me an e-receipt which confirmed my first/middle name and last name spelling.
It's a pain to change seats - I have to call and it takes at least 30 min to get someone. At least I am no longer stuck in a middle seat!