South Korea is pretty good about pumping out culturally relevant stuff too. Honestly I'd say they do it better than Japan these days (not that I'm personally interested in stuff like k-pop, but it's clearly huge)
Korea is certainly ascendant but I doubt they've passed Japan in cultural exports. At least in the US, there is anime and Sushi in basically every population center these days, whereas Korean BBQ and chicken are still mostly popular in large urban areas (where sushi is still way more popular).
Genuine question: How exactly are they more culturally relevant than Japan besides K-pop and maybe Korean novels? When it comes to matters besides entertainment, I guess I'm a little clueless.
Not the OP, but I think that's exactly what they're talking about, entertainment. I don't know if Korea has overtaken Japan in that sphere, but it's certainly significant. I'd also point out that Korea's COVID response was so organized that there was a period of time that it was being looked to and mentioned in the media which is culturally relevant (kinda like pointing out the Finnish education system or the German reputation for engineering).