Is there an area that recogonizes Korean War Veterans?

There is a small chapel area within one of the trancepts where there are insignia for all the branches of the armed forces and also tribute stained glass for veterans

I would say that the Cathedral don't have nothing about the veterans.

I feel like you're confusing this with the National Monument and wall. I don't remember seeing anything dedicated to veterans at the church. There were walls recognizing veterans outside the National Monument.