@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.
Ask me about my 70+ lists, including Omegaverse, Esperverse, Dynamicverse, and Cuteness Overload!