Yes. You did not answer the question.
Nor apparently understood the question.
Not having official diplomatic relations does not mean Taiwan is part of China. The U.S. does not recognize Chinese sovereignty over Taiwan. Pompeo reiterated that publicly just the other day.
One more time. How is Taiwan part of China?
Actually I think both mainland China and Taiwan, read the Peoples Republic of China, and the Republic of China, BOTH consider themselves the rightful leaders of China.
All of China. And Hongkong.
Mainland, and Taiwan. At least that is my understandind, having lived on both sides of the Taiwan Strait. Though that was the case a long time ago.
They BOTH consider themselves, to be in charge of it all.
Recently, there has been a tendency for some on Taiwan to consider themselves part of a free and independent country, but there is still a significant part of the Taiwan government, who think the island is the free version, of the entire Chinese government.
Two competing systems of government, even now.