But I wonder if this isn't just the US version of your Mandarin step 4. The US has dominated the global cultural conversation and the "other americans" have given up or never thought to challenge it.
...
Distantly related: I have spoken to Mexicans who are annoyed that Americans frequently (wrongly) think that only Canada and the US are "North America".
To be equivalent, it would have to be the US saying that Canadians and Mexicans were "really" just "states" of America (as Beijing insists that Cantonese is "really" just a "dialect" of Chinese) and intentionally attempting to marginalize Canadian / Mexican distinctives.
I don't think I'd mind calling Mandarin "Chinese" if they didn't then insist that Cantonese is also "Chinese", use that to gaslight Cantonese speakers into thinking that their spoken language wasn't a real language, but "full of slang", and that their written language needed to be closer to Mandarin to be "correct Chinese".
Not in my experience (lifelong American). I'm not aware of any project to make people think all of North and South America are, in fact, rightly part of the U.S.[1]
The only slightly similar thing I can recall is an impression I formed in the 1980s: the global reach of Hollywood's TV and films gave non-American's a very skewed view of life in America.
[1] other than America's Westward expansion, and as far south as the Rio Grande river. But IIUC those were militaristic expansions, not mere cultural imperialism.
Apologies, I might not have been clear.
The annoyance from Mexican friends is that Americans (apparently) often think that Canada and the US are "North America", and Mexico and southward are "South America". Or that "Central America" is a continent, and that Mexico is part of that continent.
Boiled down, the erroneous belief is that Canada and the US are part of "North America", and Mexico is part of something else.
I can't evaluate this on its merits. I have a good memory for geography, and zero confusion on this matter. Not all Americans share these traits (there is plenty of evidence for this!).
And I am not a Mexican who has ever fielded the situation with a confused American, but I take them at their word.
And, we are taught a lot of things in school that are not retained. Some 50% of American high school graduates can't find Florida on a map.
The CCP might be "engaging in cultural imperialism and suppression against minorities", but it's a stretch to claim "most" of the population is, when they have little political power and are just trying to survive.
America, of course, can also refer to two entire continents but I don't know that I've ever met anyone who's primary identity refers to their continent.
It would be very odd to me, at least, for an Argentinian (as one example) to refer to themselves as American. Same for someone from Thailand referring to themselves as Asian or someone from Nigeria saying African unless (of course) they were attempting to communicate with someone with very limited geographic knowledge (mostly Americans).
I have many friends from Central and South America and prior to meeting them I would have dismissed something like the Narcissism of Small Differences[0].
Spend some time hanging out with Colombians, Venezuelans, Argentinians, Chileans, Uruguayans, Nicaraguans, etc in a tapestry like Miami and you learn quickly it is a very real thing - going back and forth about things like how to prepare and cook beans.
At first it's very interesting to experience them (mostly playfully) poking at each other over things that most of the world doesn't notice and can't understand. However, if you know them well and they've been in the US a while when you describe the Narcissism of Small Differences they usually say something like "That's so true! I never knew it had an actual name".
When they visit the small town I'm from in Wisconsin I have to tell them that to most of the locals they're "Mexican" and to try not to get offended even though there actually are significant differences between Mexico and South America countries.
[0] - https://en.wikipedia.org/wiki/Narcissism_of_small_difference...
It can be hard to tell with Australians for obvious reasons, but I think some do hold such an identity there.
2. "Mandarin" is not synonymous with "汉语." Standard Mandarin (普通话/现代标准汉语/國語 in Taiwan) and Standard Cantonese (粤语/广东话) represent two main varieties of the Chinese language, or "汉语". [1]
3. It's unsurprising that the Mandarin speakers you spoke with refer to their language as "Chinese", considering they were addressing a foreigner and Standard Mandarin is the official language of China. However, in interactions between Mandarin and Cantonese speakers, it's common to ask, "Do you speak Cantonese/Mandarin?"
1. Born in America; it's a big country, don't know much about the outside, just call it "America" and myself an "American".
2. Gain more knowledge of the outside world, realize the world and the Americas are even bigger. Start calling it "the States" or "the US" or things like that.
3. Gain even more experience of the outside world, realize that basically everyone in the world calls it "America" and calls us "Americans", and is confused by Americans who don't. Encounter forms written by foreign governments where "American" is the only option I can choose to describe my citizenship. Start calling it "America" again.
Kind of like the "Jedi IQ Bell Curve" thing.
FWIW I went through something similar with "Chinese", but then went out the other side:
1. Don't know anything about China, call the language that Chinese people speak "Chinese".
2. Start hearing about different "dialects" within China; start calling it "Mandarin".
3. Learn Mandarin, and start reading / talking with people from China. All the people I talk to in Mandarin say "Chinese" (中文) rather than "Mandarin" (汉语). So start just saying "Chinese" in both English and Mandarin.
4. Marry a native Cantonese speaker. Realize that the majority Mandarin-speaking Han population are engaging in cultural imperialism and suppression against minorities. Start saying "Mandarin" again in English, and 普通话 (putonghua / "common speech") in Mandarin / Cantonese.