Because China is a lot more powerful than either Korea.

They can, it is just that if they do that, the PRC will sever diplomatic relations with such a country. Why that is so, you would have to ask them… neither of the Koreas has such a policy.

The situations are also not exactly the same: out of these, all are members of the United Nations except the Republic of China.

Taiwan doesn’t have nukes. Plus Korra was itself partitioned by the west. So there’s that.

The PRC has the political weight to make others pick a side, at least openly.

The DPRK, on the other hand, absolutely does not.

Because China’s assertions about Taiwan carry considerably more weight than the DPRK because China has a lot more economic and military power to lean on people with.

My understanding is that “China” is special because they’re a founding member of the UN and have special powers due to that. After the civil war, neither Taiwan or China wanted to lose that power, so neither side wanted to be recognized as anything other than “China”. I’ve heard that the younger generation in Taiwan are more open to being recognized as Taiwan but China has kind of made that impossible now by threatening any country that doesn’t respect the “one China” policy.

Partially because both of those agree on one thing and one thing only: There’s only one Korea. Recognizing one implies that they don’t recognize the other.

Having said that, some countries have managed, through some maneuvering and red tape, to have formal relations with both.

I know this doesn’t answer your question, but I think something went wrong with your formatting. In Voyager (Lemmy), your title seems to be cut off, and the body of your post is way bigger than it should be, lol