Per the 1789 census Korea's urbanization rate was 7.8%. Obviously low compared to China, which had had an urbanization rate upwards of 14% since the late Ming, or even Japan, but still far, far higher than the 3% you mentioned. The census isn't very accurate WRT larger population, to be sure, but I don't see how you're so easily assuming that Korea was 3% urban. That would necessitate a Korean population of 19 million or more in the 19th century, which is obviously impossible considering the general circumstances.
In 1925, Korea was 3.2% urban. See PDF-p. 73 here. This is said to be if anything higher than in the late 19c. At the time, Korea's population was indeed around 19 million.
On PDF-p. 70, you can also see that in 1925, only 20% of boys and 4% of girls of primary school age were going to school. (At least the way it's portrayed in the supporting docs for the 163x series, schooling was universal through grade 4 for boys in 17c Germany.)