They actually wanted to join the ISS effort, but were given a firm no and had no other option than to do pursue their own. [2]
I don't think we will see any other country-specific stations for a long time, but modular commercial stations that can be shared for research and potential business endeavors (hotels, specialized manufacturing, ...).
If efforts like SpaceX Starship actually succeed in very significantly lowering launch costs, that is. Right now it is simply not affordable either for nations or businesses. A single Starship would actually be a great temporary space station on it's own, comparable to the ISS in usable area.
[1] https://en.wikipedia.org/wiki/Chinese_large_modular_space_st...
[2] https://en.wikipedia.org/wiki/Politics_of_the_International_...
But yeah, this is definitely a reason why I hope we can keep the ISS going and just keep building on it. Additional space stations should be for good reason (for example: orbiting the moon, or - my crazy dream scenario - one orbiting in the past-GEO graveyard orbit to collect and refurbish dead satellites).
That means we should allow China to participate in the ISS, too. There are some national security concerns, apparently, but we overcame those with the USSR/Russia, and China should be no different.
Realistically, maritime law might be a better reference, given that space stations and other spaceships are informally (if not formally) referred to as "ships".
I guess it’s inevitable.