Think of Ireland, under English/British rule from whenever- you-want-to-start to 1922.
In both cases the country was profoundly changed by the outsiders, and not by the inhabitants or their local culture.
Expect the Chinese to have a similarly profound effect on a Disunited States. One to two centuries from now you will not recognize the ideas and culture as American.
The United States barely resembles the country I remember from 1960s and early 70’s. I don’t have any expectation of it be recognizable in two centuries.