I have an ex-BGO itinerary with BA, CX & QF flights. One of the CX flights is on the BA codeshare.
When I first booked, I had one PNR common to all carriers. I was able to use that to select seats through the whole trip on the respective airlines' websites - including CX.
In the past few weeks, the BA codeshare flight has acquired its own CX booking reference. My Flights still shows the original PNR with seat allocations for all legs (including the codeshare one), whereas the new PNR also shows all the legs, but with a seat allocation solely on the codeshared CX flight (which is the same seat as on the original PNR).
I haven't tried to change seats since, and my inclination is not to touch the booking in case something goes wrong. If I need to do so, however, I'm assuming the new PNR is now more likely to work.