I was in a similar situation, flying AMS-FCO-ICN, AZ ticket, AZ marketed flight, with FCO-ICN operated by KE (all flights in paid business class). I was not able to assign seats for the KE operated flight: not by using AZ’s website or app, not by using KE’s website or app. I called KE (spoke with three different agents) and the answer was “the codeshare with Alitalia uses a special tariff, which does not allow for seat selection). Not only that, but I was not even able to check-in for the second flght when web check-in opened and the biggest (and the most unpleasant) surprise was at the check-in desk in AMS (my departure airport): they could only check me in for the first flght, AMS-FCO, and told me I will need to check-in for my second flight when I get to FCO (to be clear: it’s not that the AMS check in desk could check me in but was not able to get me a boarding pass, they could not check me in on to my second flight period). The KE transfer desk at FCO was not manned and in the end I was checked in and got a seat and a boarding pass at the gate only, about 1h before departure. Needless to say, this was a very frustrating experience for me. Maybe you will have more luck than I had. And please do report back if you are able to select seats on the KE operated flights and describe the process.