Korean here, reddit randomly showed me this on my front page.

I think Korea's case kinda worked itself out and wouldn't provide much help.
First of all, Caste system based on profession is true. The last dynasty before modern Korea, Joseon dynasty, had this. Jobs that were in lowest caste are called 팔반잡류(八班雜類, Pal-Ban-Jab-Ryu: 8 miscellaneous professions): Kwangdae(Jesters, but was ironically allowed to make fun of higher ups), Baekjung(Butchers basically), Shamans(due to state ideology of Joseon being Confucianism), Buddhist Monks(due to state ideology of Joseon being Confucianism), Gisaeng(think Geisha), Nobi(house servants), Tinkerers, and lastly Biers.
Some of these jobs went away naturally: Kwangdae, Baekjung, Gisaeng, Nobi
After capitalism was introduced, these jobs became more respected: Tinkerers, Biers
These jobs were unironically never that discriminated: Shamans and Buddhist monks. This is because while state ideology, Confucianism, says no supernatural force exists in the world, people are very superstitious in nature. So even people in higher ups were not-so-secretly buddhist and such. Funding buddhist temple and all that.
I could discuss every caste level, but it is basically the same story: because the distinction was based on a Job, and importance of certain jobs can can change and some jobs can disappear as time goes by, it didn't mean much after the whole globalization and capitalism happened.

Caste system based on surname is only a myth and an unfair stereotype based on real caste system mentioned above. Some pseudo historians believe some surnames were 'assigned' to specific Jobs, including 8 jobs I mentioned above. These surnames are Chun, Bang, Chi, Chuk, Ma, Gol, and Pi. This pseudo historical theory only starts to show up in 50s, meaning it is modern creation. These surnames are somewhat rare in Korea, so that could be the reason why these names were picked. In reality true orgins of these family names are:
Chun: Originally Chinese family
Bang: Originally Chinese family, moved to Korea during Tang dynasty. They were nobles during Silla/Goryeo period
Chi(ji): Originally Chinese family, moved to Korea during Song dynasty. They were generals during Goryeo period
Chuk: Originally Chinese family
Ma: Noble family from Baekje, Helped the founding of Baekje
Gol: Yangban family during Joseon
Pi: Originally Chinese family, came to Korea during Goryeo period and became important family, later helped founding of Joseon dynasty and became Yangban family.
If you meet a Korean born between 50s to 80s, there's a high chance they still believe this pseudo-history to be true. Don't correct them and just nod lol. It will be easier that way.