I'd argue that China today is very much a different country than Mao's China, which is a very much different country than Three Kingdoms China. It is not a "multiple-millennia-old civilization".

Like, to use a simple example, "Toronto" (the location now associated with being the capital of Ontario, Canada) has been a place, a location of name, for like a thousand years. Not one political movement, not one tree, nor blade of grass, nor even genetic marker in an inhabitant from back then is there now. No memes, no genes, no scenes. Changed ownership a dozen times to a dozen different peoples. I would say "Toronto" is a fairly young city, not an ancient millennium-old municipality. So too with China. The Three Kingdoms fought bloody wars over China's ownership, it isn't a Ship Of Theseus situation, it's a "someone completely different took over, changed everything except the name in one fell swoop" situation.