[FooBarWidget]

Well Taiwan was officially given back to China by the US after WW2 ended. So maybe not inherited from Qing, but definitely from ROC.

Regarding Xinjiang, the Xinjiang claim is older than the US's claim on its own land so it cannot be more unfundamented than the US as a nation is.

[mdp2021]

The history of the USA and of Xinjiang do not seem to be easily comparable. A date for "claim" means little both in the historic context and in the context of what constitutes a Nation - a commonality of intents in a society of dwellers.