I can't think of any reason for Korea to get a science boost to them, from a historical perspective. It would make sense if they got science with stability (as their golden age of science happened in their 200 year period of isolation and relative stability compared to their neighbours (*cough* Japan *cough* China), but I don't really see where the idea of water being a boost to Korea is from. They have the invention of Jang Yeong-sil's water clock but that is really the most I can gather for water and science interacting in Joseon Korea.

I am not well-read on Korean history though so would appreciate anyone taking the time to help me learn the reasons why. A side note, I really like how HK handles their turtle ships, it is much more realistic than how Civ handles them.

I don't think the devs were thinking of it as long as you tbh. I would say they just had to think of a science-boost legacy trait and coastal water came handy because Korea is already presented as a sea culture with their emblematic unit, and I don't think they could go with a different unit because turtle warships are heavily referenced in pop culture when discussing Joseon Korea. Sometimes game mechanics will be more focused in in-game synergies than in historical accuracy. I personally don't think it is necessarily bad unless it is super jarring.