I do not. That was the whole point of my multiple comments in the original thread. America is the correct noun, in English, to refer to the United States of America.

We can get into definitions of continents if you like. I accept that people from Spanish- and Portuguese-speaking backgrounds primarily talk about a 6 continent model consisting of America, Europe, Asia, Africa, Australia/Oceania, and Antarctica. I can also accept that because there's no real solid definition of a continent, it's impossible to say that this is wrong per se. I will say that I find it an absolutely baffling grouping to use, and that I myself prefer 6 continents consisting of North and South America, Eurasia, Africa, Oceania, and Antarctica; it makes no sense to me that someone could group the Americas while considering Afroeurasia three continents: to me, either an isthmus like Panama and Suez separates continents, or it does not, and it's weird to split over Suez but not Panama, and even weirder not to merge Eurasia who have no physical separation. (And IMO, once you start separating Europe and Asia, it becomes hard not to justify separating Arabia and India, if we're trying to keep a logical definition.) But continents aren't especially logical. In most of the English-speaking world, the 7 continent model dominates. We talk about North and South America, Europe, Asia, Africa, Australia/Oceania, and Antarctica. Those are the 7 continents, and while you can disagree with them (as I do!), in most conversations you're just being difficult if you bring up that disagreement in anything more than a very lighthearted way.

The use of the demonym America stems in part from that. Once you reject the notion that "America" is a single continent, it becomes far easier to understand that the demonym "American" can't refer to people from two continents, and so it's very normal to use it to refer to just one country. That country being the United States of America. It's pretty normal to refer to countries by their short form. Czechia a few years back started a big campaign push to specifically ask people to call them that, rather than always using the formal "Czech Republic". Australia rarely gets referred to as the "Commonwealth of Australia", and the fact that Canada is officially "the Dominion of Canada" is rarely even acknowledged by official texts these days. Amusingly, America's southern neighbour has an equally valid claim on the name "United States", since Estados Unidos Mexicanos translates to United Mexican States, or, roughly, United States of Mexico. Latin Americans often get upset at this because in Spanish, the demonym is 'estadounidense', which roughly translates to 'United Statesian'. But that's not a word that exists in English. It's not especially logical even in Spanish, given that logically speaking, estadounidense could also refer to Mexicans. But words are defined by their usage, and in common usage that word unambiguously means American. The same is true in English. American unambiguously, in English, means person or thing from the United States of America. It's silly to get upset by that.