@Le*** I have a list called "Otherverse" that includes both Cakeverse and Nameverse, and I just checked it, and so far, all the Cakeverse are Japanese manga, not Korean manhwa. It's still a really new thing (compared to 99% of other BL categories) so I'm sure if you give it time, Korean Cakeverse will eventually show up.
Omegaverse
https://mangabuddy.com/manga-list/206933
Esperverse
https://mangabuddy.com/manga-list/206951
Beastverse
https://mangabuddy.com/manga-list/206934
Ask me about my 60+ other lists!