This is actually an exceedingly important thing to clarify because the failure of the USSR in losing the narrative on its collective Soviet identity is one facet of how the state was partitioned into ethnic splinter nations after its collapse. Of course, one particular challenge there was that the Soviet identity was always entirely artificial, whereas Chinese identity has been built on thousands of years of collective history.
This is why Western "Sinologists" are obsessed with chipping away at the peripheries of historical China and "othering" them as foreign groups, stripping away the Chinese identity of the Liao, Yuan and Qing and reducing being "Chinese" to essentially being "Han." If you read the seminal academic publications in the Western field like the "Cambridge History of China," you'll find that this thesis is one of their major preoccupations: the historiographical partitioning of Chinese identity.
As the Chinese saying goes, important things need to be said thrice:
Chinese culture =/= Han culture.
Chinese civilization =/= Han civilization.
Chinese people =/= Han people
Modern national states are built around a conception of ethno-nationalism. France is for the French, Poland is for the Poles, Greece is for the Greeks, etc. This is not how Chinese identity is formulated and this point is so important that the framers of the Constitution saw it necessary to explain this within that document:
"The People's Republic of China is a unitary multi-national state built up jointly by the people of all its nationalities. [...] In the struggle to safeguard the unity of the nationalities, it is necessary to combat big-nation chauvinism, mainly Han chauvinism, and also necessary to combat local-national chauvinism." - Preamble para. 10 of the Constitution of the People's Republic of China (amend. 2018).
The simplest way to understand this from a Western standpoint is recognizing that Chinese identity is more like that of the ancient Romans than modern ethno-national identities. Yes, the Latins/Italians built Rome and sure, Roman culture, governance and language pivoted around this Latin/Italian influence, but by the time of their empire, being Roman was no longer being just Latin/Italian. Spaniards, North Africans and Syrians were Romans too and they ruled the empire as as its emperors. Kublai Khan was a Mongol not a Han, but he belongs to China in the same way that the Spanish Emperor Trajan belongs to Rome despite not being Italian. Although some groups completely assimilated into Latin culture and language just as what occurred with the Han, that isn't a precondition for being Roman or Chinese.
It shows the enduring power of such collective identities (and why China's must be protected from revisionist assault by both internal ethno-nationalists and external Western "Sinology") that eventually, it was the non-Latin "Greeks" that would carry the torch of Roman identity for another thousand years after the Latin West completely fell to the Germans. There's even a famous anecdote that when Greek soldiers liberated Lesbos from the Turks in 1912, the locals were astonished that the Greek soldiers claimed they were all the same people, responding that: "You're Greeks, but we're Romans!"
