In recent years you've had obviously BTS on the music side of things, Parasite with films and Squid Game with TV shows being absolutely huge.
All 3 are essentially the magnus opus in their respective fields for South Korea internationally. But another aspect of South Korean entertainment that's pretty unique are their variety shows.
There's obviously a much higher barrier (due to multiple reasons) to international success with variety shows so at most I can never see one getting big outside of East Asia, but even in that regard unless I'm missing an obvious one no show has got anywhere near the popularity of peak Running Man there either. You're talking a peak that was like 6/7 years ago in my opinion as well.
With the variety scene not what it used to be in South Korea anymore is the answer - it's very likely it'll never happen?