The Quebecois as a faction currently do not govern Canada at all

That's not the point. I guess you could argue that's the point, but the point of the counterfactual was to demonstrate how, if partitioning states with puppet governments could produce new states then the US would be doing it to contiguous land masses. Taiwan feels different because it's an island, but it's not really that different from doing it on contiguous land.

the Canadian government does

Sigh. I'm so tired of explaining category errors to you. The Canadian government is a role. The role is currently played by the parties involved in governing Canada. There is a Quebecois faction in those parties. So because of your category error, you are wrong. The Quebecois, by participating in the government of Canada DO in fact govern Canada. But that's not as relevant to my point as you make it out to be.

Similar to how the CPC did not govern China

Again, not relevant to my point. Because for whatever reason, you think that it's relevant to discuss whether the CPC had a claim to the seat of the government for this discussion. It's not. New parties form all the time. Just because they didn't exist before doesn't mean they cannot become the government after. I swear it's like playing Calvinball with you (and not just you, everyone who wriggles about on this topic does the same thing). The reason the CPC did not govern is because they were violently purged by the KMT, which is what caused the civil war in the first place. Again, would you say that Democratic Socialists of America cannot govern the US if they take power (either by election or otherwise) simply because socialists were purged from the US (twice)? I wouldn't say so.

Revolution is a valid form of seizing power within a state.

The CPC, as mentioned, understands it differently from you, as they by their own words founded a new state.

Yeah. Unfortunately we're just going to have to disagree on this. The CPC didn't even have the power to do such a thing. What they founded was a new republic. That's different than a new state. Again, there is not precedent for a revolutionary struggle creating a net new state without secession, except in the case of the USSR, but it did not eliminate the prior state of Russia. Russia remained a state and joined a net new state called the USSR.

You really can just read the literature. "China became communist". "China became a one-party state". Etc, etc. All of the literature establishes that there is this state called China and it transformed through various transitions while still maintaining its existence as the state of China. It did not dissolve. It did not splinter. It did not seceded. It did not divest. It did not merge. It remained the state of China. You're doing to have to bring a lot more than "this English translation of the words of the CPC prove that its a new state".

Coups are different than civil wars, as with a coup a faction seizes control of an existing governmental structure. A civil war is a more fundamental break. And there’s plenty of precedent in this. Take the American Civil War

They aren't as different as you think. China certainly follows the model of a coup far more than it follows the model of the American Civil War. I'll reiterate, the CSA seceded from the Union. No such thing happened in China. Instead, the CPC fought the KMT for the existing governmental structure.

the CSA can’t really be considered the same state as the United States

Because it seceded, formally.

Had the civil war ended in a stalemate, they likely would have remained that way.

Because it seceded, formally.

But if the CSA had won and annexed the US, there’s a decent chance they’d consider themselves the legitimate continuation of the US (despite having declared a new constitution, like the CPC did).

They wouldn't have because they seceded, formally. They had no interest in annexing the Union. But again, new constitutions happen within states, not between two states. That's how revolutionary change works. There are dozens of examples of countries adopting new constitutions but not becoming net new states. Surely you understand this.

Regardless, the problem is that civil wars are messy. Take the Vietnam war. Technically French Indochina was split into two Vietnamese states, yet the Vietnam war is considered a civil war and ended with the “reunification” of the two states. You can endlessly debate definitions, but none will see definitively fit all of history.

I mean, it's pretty clear exactly what's going on there, right? European Imperialists arbitrarily divided a nation-state, and despite that division, the mechanisms for defining a nation-state supersede the imperialist intervention. There was in fact one Vietnamese nation-state that the French arbitrarily split apart creating two net new nation-states that the international consensus recognized (because imperialism) but when the war broke it all of the analysis agrees that it was actually a civil war within a single nation-state ending when the integrity of that nation-state was restored. You can see it for Vietnam, but you can't see if for China. You're arguing my points, but you just can't give up the moral position that you don't believe the CPC is good and because you don't believe it's good you can't possibly see any argument that would promote the position it has.

Even in China the lines are blurred

Obviously

Since 1991 the ROC does not actually regard the PRC as a rebellious group, and abandoned its claim to be the sole representative of China

Yup, because it realized that it can't maintain the international consensus. It was a conciliatory move towards the PRC.

But the PRC has not responded in kind, not acknowledging the ROC as legitimate

And this is problematic because why? Because the ROC deserves to be considered legitimate despite losing a civil war and then prosecuting the White Terror for 40 years while under imperialist protection? The PRC has not responded in kind because it has no need to. It is in the right.

De facto the war has ended

That's a correct use of "de facto" for sure! Yes, the war has ended, de facto, but it has not ended de jure. And of course, what is the end of a war in the de jure sense? Mutual agreement. Terms of surrender. In essence - law. That has not happened yet, so the war is de facto over but not de jure over.

yet there’s no one party now in control of both the mainland and Taiwan

That's also correct. Because, again, the war has not ended de jure because de facto Taiwan is a protectorate of the imperialists who seek to continue to exploit and subjugate China.

It’s solely diplomatic pressure from the PRC that is preventing countries from acknowledging this (even though they do have embassies and such in Taiwan, so it’s de facto accepted).

Yes, the PRC, the current government of the nation-state of China, of which Taiwan is a part, is refusing to acknowledge that there is a separate nation-state and Taiwan is not demanding that it do so. The only people demanding that it do so are internet quarterbacks. No government has asked China to recognize Taiwan as independent. There are no claims of independence for China to recognize. And, I'll argue your side, China has stated that if Taiwan should announce secession, it will invade. It does not recognize the right of the people on the island of Taiwan to secede from China, much like the US does not recognize the right of any portion of its country to secede. The only nation-state that I am aware of that has ever established a right to secede is the USSR. As for the embassies, they are the form of diplomacy. I don't know that it makes sense to read into it. Embassies exist for non-nation-states all over the world.

Civil wars that don’t de facto end in a reunification are typically considered to have spawned separate states (e.g. North and South Korea for example, or North and South Sudan).

Yeah, I just don't think that's true. Korea was partitioned by, you guessed it, American imperialists (yes the USSR agreed to it because appeasement was their best option). It wasn't a civil war that caused a partition and didn't end in reunification. North Korea still considered South Korea to be an occupied territory, which generally speaking is pretty true. The Japanese occupied the peninsula, the Americans occupied it. The Americans drew a line in the sand like Yosemite Sam and dareds the Koreans to cross it and then they bombed the entire northern part of the country to rubble. South Korea was occupied, then the Americans established a fascist vassal there, and is now a vassal state of the US. If reunification happens, what will result is the ORIGINAL nation-state of Korea, out from pages of history. North Korea and South Korea as states will cease to exist, but the original nation-state that the imperial Japanese, and subsequently the imperial US, stomped on will return. Just like in your Vietnam example. You understand this for the examples you're OK with. You have cognitive dissonance for China, and I assume for the DPRK, because of your moral framing.

But even if they do the lines are blurred; is Turkey the same state as the Ottoman Empire? Or is it a successor state?

No, because the Ottoman Empire, like the Roman Empire, was formed during the time of city-states. The Ottoman Empire would be contiguous with Istanbul, like the Roman empire would be contiguous with Rome and the Holy Roman Empire would be contiguous with the Vatican. In fact, the interesting question would be whether the Holy See is in fact contiguous with the Holy Roman Empire. I think it might be. But that's the only interesting question along these lines you've raise. Every example you raise fits quite well into the framework of Westphalian nation states (which Rome and Istanbul were not).