
Sexually Transmitted Diseases were known about back then (though depending on the time period and location people may not have known that these diseases were transmitted through sexual intercourse), and common.
fun fact: One reason wigs became fashionable in Europe in the 1600/1700s is because of Syphilis-related hair loss.

I believe that this comic takes place during the Joseon Era (1392-1897) so it's very likely that syphilis was already in Korea.
One major theory about the origins of "Syphilis" is that it was transmitted from the Americas to the "Old World (Europe/Asia/Africa)" after contact in the 1400s. Portuguese traders introduced syphilis to China in the 1500s, and considering the close relationship between China and Korea I'm guessing Korea also had its first cases during that time.

by tell do you mean that it is difficult to tell what STI's the ancient written sources are referencing? because that is very true, but one way we do know about the existence of syphilis in different time periods/locations is there is evidence of the disease in bones of deceased people from those periods of time and locations.

I think they had a very hard time differentiating syphilis from other diseases since even today we have to confirm it via blood test, its symptoms are similar to other diseases. I'm sure they were more likely to recognize diseases that cause very obvious signs on genitalia as Stds.
As for skeletons, I mean, they only find so many ancient skeletons since they obviously don't remain intact, it's only through medical and artistic writing and images that we know a lot of the things the ancients knew of.
But do they not have sexually transmitted disease back then? (Rhetorical) just stick to one dude