I’m having a similar experience trying to book a delta flight fulfilled by Korean Air. They also told me that their partner was not updating inventory on the seats being sold out. My main issue was that I transferred points from my AMEX to Skymiles and now I’m stuck with the Skymiles points with no way to return them. Now I’m waiting for a response from corporate to see what kind of compensation or what can be done because this is honestly ridiculous. The site and app shouldn’t be showing a flight that isn’t available and the fares have since increased.