In the case of BA, in my experience, even before all these interlining changes, they never were efficient or pro-active in case of IRROPS when separate tickets are in the same PNR. For example, last year I flew QF to LHR with a connection to ORY on BA. All flights were on the same PNR (travel agent did it), but the QF ticket was MEL-LHR-MEL and the BA ticket was LHR-ORY-LHR-ARN. The QF flight arrived 4 hours late and I missed my flight to ORY. At first BA asked me to pay the no show fee, fare difference, etc.. I had to argue for 10 minutes and it somehow got fixed, but they flew me to CDG and I only saw my bag 3 days later in ARN.
On the other hand, I recently flew MEL-LHR-ARN QF-BA on the same ticket. I missed the BA flight and BA had already rebooked me on a later flight to ARN and re-tagged my bag. So in my experience, with BA, it makes a big difference if the connecting flights are from separate tickets even in a single PNR in case of IRROPS.
I even had the agent in the BA F lounge tell me that BA doesn't protect connections with separate tickets in a single PNR...