The governments of Texas and Hawaii don’t pretend to control the entire United States.
The China/Taiwan thing is downright silly. They can pretend all day long and make all the claims they want, but at the end of the day it’s just make-believe. The PRC doesn’t control Taiwan, and Taiwan doesn’t control the PRC. The rest of the world will smile and nod and say whatever we have to in order to get what we want, in the same way you’d smile and nod until your crazy neighbor stops ranting and goes back in his house.