Well, specifically regarding 華 and 華人, if you want to watch something interesting, ask a group of Mandarin speakers that aren't PRC citizens whether they're 華人. 9/10 times they will immediately begin arguing with eachother about the answer. That's basically my point: 華人 and similar concepts in English described as "Chinese" have been historically defined by empires, written about by empires, etc, and modern anthropological techniques are finally teasing apart that this concept isn't necessarily natural but more derived from the efforts of any given empire in Chinese history - all building on eachother and legitimizing their given rule using these historical concepts. I certainly don't disagree with you that there's a lineage of these concepts!

> DNA tracing has established the genetic continuity of a Han race going back thousands of years, with an extremely homogeneous genetic profile between members of the race.

This seems to me to be an oversimplification of even the "well accepted standards," such as for example there's a clear delineation between northern and southern "Han." You can subdivide Han even further purely genetically. Furthermore, at the end of the day, defining race by genetics is always a bit of a rabbit chase since it's a relatively meaningless distinction without considering culture, and culturally, the group most call "Han" is extremely diverse, much moreso than portrayed historically or in the modern era. I won't go into the trouble of listing the distinctive ethnic groups, many of whom aren't even recognized by the CPC, but suffice to say basically every province has one or more distinct ethnic groups normally described simply as "Han," and that's before counting what the CPC (and others) designates as "aboriginal."

> Next most definitive is the language.

I would say this is the least definitive! The unique nature of a morphosyllabic language is many languages can be written with it. Yes, definitely the various languages of the cultures within the PRC's modern territory are unarguably similar, but that's a feature shared with various languages in other parts of the world. Take a look at India! So, for that reason, just because many different people throughout history could read what was being written by whatever Chinese empire, doesn't mean they were all Han via language.

Further to that, the reason that people in Taiwan, the PRC, Singapore, Malaysia, and throughout history Korea and Japan, could speak what we today call Mandarin, is because it was the language of an Empire. Of course one would speak the King's language in the King's land.

I mean, in the PRC they call every language "Chinese" when speaking about them in English - Shanghainese, Ninghainese, Ningbonese, everything. So it's just another empire doing empire stuff.

> Culture is the least definitive concept, but it's very plain you have a shared culture. It's not exactly the same (and culture varies within a country too) but historically it is very clear it comes from the same culture. Frankly it's quite a basic fact that the people on Taiwan and China have historically been part of same people.

With all due respect, just saying this doesn't really refute my argument.

> both what might be called the "CCP Han identity" and "Taiwanese identity" are political movements.

Yes, this is an overall point I have, that these concepts are difficult to divorce from politics, since politics has such a strong effect on what these are. E.g. if it weren't for the politics of the early United States, many indigenous languages in north america would be much more widely spoken (a recent news item I learned about, it's on mind) - regardless of the initial conquering, it was specifically the political policy of reeducation that ensured the basically permanent demise of these cultures.