Other than that, I agree with your assessment: Taiwan's thriving democracy undermines and contradicts the Chinese Communist Party claim to power, in particular the CCP's narrative that democracy is neither needed nor wanted, nor desirable for the Chinese people.
It enjoys independence and autonomy, but the rest is so nuanced to instead be a complete mockery to the whole nation state concept.
I don't think its worth debating. You can negotiate directly with Taiwan, and accept their rule of law to navigate business. Isn't that all you need to know?
some people in Taiwan would be offended by saying "Taiwan, China" by assuming that you are saying it is a province of the PRC. other people in Taiwan would not care, while yet other people in Taiwan would appreciate that you recognized that Taiwan is the legitimate China and you just wrote the Taiwan part for descriptive purposes, ALL WHILE you are just trying to maintain consensus with the other people you work with which includes your own country and also the PRC, and then a random Taiwanese-American will call you "racist" for "mistakenly" thinking their heritage is from "China" instead of Taiwan, projecting their own exile as part of an amorphous underrepresented Asian-American diaspora amongst ignorant foreigners, and its like "no, buddy."
Occam’s Razor.
Taiwan is de-jure a part of China. China just happens to be in the curious state of having two competing entities claiming to be the legitimate government.
Both ROC and Beijing agree Taiwan is China. The “C” in ROC is China!
But many mainland Chinese do, and the government spends considerable effort cajoling/bullying the rest of the world to not recognize Taiwanese sovereignty. From what I can tell there is a real threat China might sometime attempt military conquest.
Anyway it’s complicated. Some in ROC want independence. Some don’t. Some would like to join Beijing (many investors from ROC). Most probably want the whole thing to be on the low and the ROC ignored lest the dragon is awakened.
But regardless what civilians want, being part of China affects the actions of Taipei more than any other issue.
When Japan lost the war, Taiwan was governed by the Allied Powers, who appointed Chen Yi from the Kuomintang (KMT) as chief executive and garrison commander of what was called "Taiwan Province". The Peace Treaty with Japan (Treaty of San Francisco) and the Sino-Japanese Peace Treaty (Treaty of Taipei) both did not specify that Taiwan was a part of mainland China. I think formally/legally Taiwan was Japanese until 1952 but Japan was under allied control at the time. The question of Taiwan's legal status was left open in the aforementioned peace treaties. This is the legal/technical root cause for the problems with Taiwan's legal status even today.
So, as far as I can see: de facto Taiwan is an independent nation. And de jure it's ... unclear.
Finally, let's bear in mind that in a very real sense there is no such thing as "international law", much of what is called international law is really just voluntary consent of states.
(Taiwan probably also sees this as a bargaining chip, to be given up at an opportune moment (like the Kinmen Islands), in exchange for something else, e.g. China accepting Taiwan's independence. I suspect this would have been possible at some point when China was weak but seems unlikely now.)
Depends on the view. The central Chinese government certainly considers Taiwan to be its province, and achieved that Taiwan has no seat in the UN, and sanctions Hotel chains that treat Taiwan as separate country. Taiwan themselves maintain a claim to the entire mainland as well, they just disagree on who should hold power. There are also countries that recognize Taiwanese independence, as there are countries that recognize Taiwan's claim over of all of China.
but that's a close as they ever got to having their flag fly on taiwan...
Take a stroll by these.
Another note: History is written by the victors.
This isn't the whole truth I don't think. They do maintain officially maintain this line... under the implied threat of invasion/war from the mainland if they deviate. Similar to how he US officially doesn't recognize Taiwan as a country because it isn't in the US interests to invoke hell's fury from the PRC over Taiwan, but for all intents and purposes the US treats Taiwan as an independent state.
The DPP (plurality party in Taiwan) generally leans towards viewing Taiwan as an independent nation. The main opposing party's view is generally consistent with what you've stated in my understanding.
It's a complicated topic but you're mainly projecting the main land's view onto the people of Taiwan.