A CRS/GDS locator (PNR, the 6-digit alphanumeric code often used to identify tickets, but really only points to a GDSs database entry) and a ticket are not the same thing, though. A PNR can include non-air travel segments like hotels and rental cars too, for example.

That's something very different from a single airline issuing a ticket for a complete itinerary, which importantly makes them responsible for getting you to your final destination in case of missed connections, checking your baggage through etc.

If you still have the confirmations or boarding passes, you could check for the three-digit numeric e-ticket number prefix, which defines which carrier actually issued the ticket.

JAL (JL) and Quantas (QF) are both members of Oneworld, so they can share itineraries (and things like frequent flyer status and fare class) in a single booking regardless of codeshare.

Isn't it entirely dependent on the airlines, what counts as one itinery? How could I contractually obligate them to something they didn't agree to be contractually obligated to?

(BTW: I've had multiairline itineraries many times. I think a lot of airlines are perfectly happy to do it because they can't fly domestic in that country and the domestic airline doesn't fly international. Also, there have been times when I haven't been able to, and I've been worried about it, and I got to the airport for manual checkin, and they've said "oh, i see you have an ongoing flight to such-and-such, do you want me to check you in for the whole journey?")

Nope, they can't, either the GDS allows booking it in which case it's already possible or the GDS doesn't allow booking it and then no app can do it. There are plenty services already which allows you to book the craziest itineraries. Like, ITA Matrix Powertools can construct a clickable link into Orbitz from ITA Matrix searches and it doesn't get crazier than that. There's Bookwithmatrix too.