When you talk about these, please remind yourself that you are talking about a subject matter of comparative civilizations. China is not part your western civilizations, it does not want to be, and it never will be. China is not Japan or South Korea. China is China. Don't use the norms of your own civilization as a universal rule, because they are NOT.
China is NOT your typical nation state, which is a concept founded in the history and political science of the Europe. China is China, and China has always been China. Traditionally, China is not called a country, it was called an imperial court "天朝". Read enough Chinese history and literature, and you will know that traditional Chinese do not usually refer to their "country" as a country ("~国"), it was referred to an imperial court, or imperial dynasty. The idea of "country" has always been subservient to the idea of "the imperial court".
I think this is because China has many countries: Wu (吴), Chu (楚), Bashu (巴蜀), Qilu (齐鲁), Qinchuan(秦川), ....etc. These are the countries (国). China is above that. This is not just a simple territorial divide. Without the idea of China above, these "countries" can form their own organic nation states. These don't even have ethnic/racial divides like the Turks or Tibetans. They are all part of China simply because China is not a nation state. China is a civilizational state.
There are no existential conflict between China the civilization state, and the many little Chinas the (could-be) nation states. Because the idea of China is not on the same level of the nation state. Chinese people are born and raised with the awareness that they are sharing country with distinct people they have little commonalities with. I was aware of this as early as in elementary school. I was born in the city of Wuhan, basically in what I would call the Chu (楚) identity. I instant felt foreign when going to Jiangsu (江苏), or Guangdong (广东). But, I didn't feel foreign at all when going to Hunan (湖南) province, or anywhere else in Hubei (湖北) province, or south part of Henan (河南) province. I don't understand Henan or Hunan dialect/languages, or even some local dialects within Hubei province, but I didn't feel foreign there. But for Jiangsu and Guangdong, I did feel foreign there and I don't understand their language/dialect.
Similarly speaking, some neighboring language-culture regions within China forms a cluster, even if people don't typically understand each other's dialect, but they are close enough that they feel akin them. You will see people in Guangxi feeling a lot more kinship with people in Guangdong than the people in Guizhou. People in Fujian would feel a lot more kinship to people in Taiwan than people in Guangdong. This is the idea of the country, the nation state.
China is none of those could-be "countries". For the Chinese to put their Country above the Party (which is heir to the concept of the imperial court), they will only end up destroying China. Because their concept of a country is a bottom up concept, based upon each of their could-be nation states. This is why the Party is above the country. Because the without the Party, there is NO one country of China.