Korean Air code share checked luggage

I just booked a Delta flight to Singapore with a Korean Air connection in Seoul-Inchon. The Delta legs are Comfort+ and Premium Select but the KAL leg is apparently basic economy. Apparently no seat selection is available until 24 hours before the flight and perhaps not until check-in. Ahhh, such is life.

QUESTION: Delta allows two free checked bags. If we check luggage with Delta will it be checked through to Singapore or will we have to retrieve it in Seoul and re-check it with KAL for a fee?