For example:
Probit exchange has https://coinmarketcap.com/exchanges/probit-exchange/ for global and https://coinmarketcap.com/exchanges/probit-korea/ for Korea (South Korea).
Huobi exchange has https://coinmarketcap.com/exchanges/huobi-korea/ for Korea and others for some countries like Thailand, Indonesia, Argentina.
I also don't think crypto is illegal in Korea, I don't know the 2 exchanges you mentioned in Korea but I think we all have heard of the quite famous exchange Upbit. They are in the top 5 largest exchanges and are also one of the reputable market makers in the market. Also, let's not forget that Do Kwon, the founder of Terra, one of the projects that collapsed in the summer of 2022 is also from South Korea. So it can be said that cryptocurrency is not only not illegal but also a fairly open market for this industry.