What's missing from this is China making a lot of soft calls to SK, basically saying 'we like you, we can pressure NK into a more peaceful position, invest with us, we're all Asians', and SK seems to be responding positively.
SK being closer to China would be a game changer for geopolitics, and they would need _very strong_ guarantees from China, so strong I don't think it's possible in the short term (unless NK has a regime change).
Do not assume that the rest of the world follows the US view of ethnic identity. Groups that would all be classified under “Asian” in the US would be considered different races in China. Regardless it is true that the PRC, even despite political differences, would be more in tune with the ROK culturally due to the long history of Korea falling under the influence of the Sinosphere which is something the United States should be more wary of as a competitive disadvantage when trying to maintain influence over the region.