You missed my point. Regarding the HRE, the point wasn't that it's sole histotical original location was the Holy See but rather that it is one of the few remaining city-states in the world. Regarding the Ottoman empire, the people were Turks but they were organized into various tribes, many of whom were nomadic or being displaced by conflict with e.g. the Mongols. A specific tribe which had settled down for about a century was not the entire Turkic nation, and no one would call their 150-year settlement a nation-state. They became the Ottoman Empire around the time they took Constantinople, and did not establish a Westphalian nation-state, so the idea that the modern nation-state of Turkey would be the same state as The Ottoman Empire doesn't make sense. I agree that saying the Ottoman empire is equivalent with the a city-state located in Instanbul is not correct. My point was that your questions have answers that can be distilled from analyzing history. Should the nature of society collapse back to city-states, along with all the conquest-driven empire building, I think a city-state in Instanbul could claim inheritance to the Ottoman Empire, given a bunch of other conditions, and I think other city-states and their empires would likely recognize them.
Regarding China - you are correct, it is not a nation-state in the narrowest definition of the word as used by the Westphalian system as it was originally articulated. But by the same standard the US is not nation-state, nor is Canada, nor is any country in the Western hemisphere except maybe Haiti. So while you are technically correct about a very specific narrow definition of China's status as a nation-state, you are fundamentally incorrect that it does not participate in the social construction of nation-statehood. It is a nation-state in the same way the the US, Russia, and India are nation states, despite them not actually meeting the exact criteria of a nation-state in the strictest sense of the word. This is important because international "law" and relations does not see a mechnical difference between a nation-state and a civilization-state, nor between a nation-state and a settler colonial state, nor between a nation-state and a plurinational-state. Maybe one day the world will operate differently regarding these things, and if it does I would assume the claims of China as a civilization state would carry significantly more international weight than the claims of the settler colonies in the US, Canada, Australia, etc.
Interestingly it's a perspective the CPC is keen to avoid (since it's not very "socialist" after all).
Hmm. This is a tangled mess of a sentence. Nation-states are quite socialist. Lenin's work on the national question is very socialist. The idea of national self-determination, that is the self-determination of a nation of people not of a nation-state, is quite foundational to socialist politics. Nation-states are a clear mechanism for national self-determination in the current global order.
The CPC has been keen to avoid the narrative of being a nation-state, that's true, because they are working on a narrative that is older than most of the systems that invented the nation-state system. But Europeans conquered the globe and this is the system China finds itself in. It has very few claims if it is not recognized as a nation-state (however inaccurate) by the majority of the world's governments. From the lens of the European governments and the UN, China is a nation, and it is a nation-state, and they deal with it on those terms. The Han on the island of Taiwan are not a distinct nation from China and the government of the island of Taiwan claims to be the same nation-state that the government of the mainland claims to be. There is only one nation-state, from the perspective of the North Atlantic world order, that is being claimed by both parties. There are not claims of the existence of 2 distinct nation-states (again, of the form understood by the current North Atlantic world order) except by Western chauvinistic citizens with no power except to rage at the immorality of others to avoid the immorality they are a part of.
If nation-state talks sounds nationalistic and imperialist, it's because it comes from the European nationalistic imperialism that has been subjugating the world for the last 600 years and subjugated 80% of the world's population at its height. We're still coming down from that. Decolonizing, as it were. Part of that is refusing to play into the hands of the imperialist North Atlantic on the topic of Taiwan. And not for nothing, it seems clear that both the leaders in Beijing and the leaders in Taipei understand this which is why they are using the language they are and why they are making the claims they are and why they are NOT doing many of the things Westerners think they are doing or should be doing.