The fact that the US has indivisibility in it's constitution is a weird historical wrinkle, and one I find hard to reconcile given that they chose to separate from Britain. How they didn't recognise a general right for self determination is beyond me. But then I am a Brit.
I'm married to a former Chinese citizen and have family in China, and while Ive not lived there I've been many times. It's oppressive enough of minorities just in the relatively peaceful areas I've visited. There's a superficial respect for ethnicities, but that's coupled with a sustained campaign of cultural suppression, dilution and colonisation.
For example there's no smallness of degree of ethnic blood too thin to count as part of that ethnicity, and ethnic groups get privileges Han don't, encouraging registration as minority members. Plus registration is just a matter of getting 'notorised', which is an unbelievably corrupt system. The result is that the vast majority of official members of 'ethnic minorities' have virtually, or actually no connection with the ethnic culture, but get full say in how their 'minority' is represented and treated. All the people who get an official say in minority relations are functionally 100% Han, and party members to boot.