Back in reality, the Republic of China (Taiwan) is fully independent from the People's Republic of China and fulfills every criteria of nationhood.
Facts on the ground appear otherwise, but facts on the ground also imply that Taiwan is not part of the PRC's version of China.
No. I don't understand how you came to this conclusion. Both governments claim legitimacy and only one has actual sovereignty.
Taiwan is an independent country.
Taiwan is an island. It is still China. It is impossible to both give deference to the ROC and say otherwise.
That isn’t what the facts on the ground are though. The ROC no more has sovereign jurisdiction over the mainland than the PRC does over Taiwan. Which is to say that at this point they are functionally separate sovereign nations independent of each other, regardless of the claims by either the PRC or the ROC. Or put another way, the way I did the first fucking time: Taiwan is an independent nation.