> No, they sound like Taiwan is part of China, something the entire world and Taiwan itself officially recognizes.

That presumes the "official" position is the genuine position, which is often not the case.

With regards to Taiwan, "official" positions are often lies tied in knots to appease Mainland China's sensibilities.

There's an endless number of internal and international reasons beyond appeasing the PRC.

Such as?

It is the basis of US-Taiwan relations as a starter.

> It is the basis of US-Taiwan relations as a starter.

Only in the context of the PRC. The reality of US-Taiwan relations would be much clearer if it was not PRC policy to sever diplomatic relationship with any country that recognizes Taiwan.

On the topic of Taiwan, it's a mistake to reason about de facto relationships from de jure "official positions." Basically, the "official positions" are lies, and the actual positions are not directly stated.

> It's like the US had a civil war and the losing side flees to Hawaii and in 2090 we still arguing whether it is part of not of US or should it declare independence.

That actually sounds like a very plausible counterfactual to someone outside the US.