You are not wrong that Taiwan is part of China according to official definition (from both PRC and Taiwanese gov).
However, "Taiwan is literally the Republic of China." is disingenuous considering that their government is not the one that sits in the United Nations.
I don't want to get involved in politics. But I have to point out "Taiwan is literally the Republic of China." is 100% correct. The official name of Taiwan is Republic of China (ROC). On the cover of Taiwan passport, you can only see Republic of China. The interesting thing is the claimed territory of Republic of China includes the China mainland and Mongolia, not just Taiwan island. The official name of China mainland is People's Republic of China (PRC), literally same to Republic of China (ROC). It's too complex for western people to understand. Just refer them as China and Taiwan.
I am from China mainland, having friends and colleagues from Taiwan. Don't want to see wars happen between PRC and ROC.
When people refer to China, they are referring to mainland China which is about the same size as the continental US, and not a small island about the size of Vermont. They are two different things because Taiwan based businesses do not have the same access to mainland China vs businesses based on the mainland. China's domestic market is pretty much a closed one.
However, "Taiwan is literally the Republic of China." is disingenuous considering that their government is not the one that sits in the United Nations.