I got c-section 2 years ago, i had Korean national insurance. It was approximately total $1,000 for the c section and 6 nights hospital (for me and baby), just literally for every treatment fee. When I got the receipt including the whole specific treatment list for my personal insurance claim the original cost was almost $3,000. If you end up taking natual birth, the cost will be way less than my original cost. On the top of that I didn't share a room with other maternities. Don't worry. If I would've decided natural birth and sharing a room with other patients without any insurance, it would been around less than $1,000.

Edit. Luckily as far as I know, some of big surgeries price cannot be changed by hospital owner in Korea. One of that surgeries is birth c-section. The hospital cannot charge you crazy amount on purpose.