Lexico's definition of Usonian presents it as a perfectly normal synonym for American:
Relating to the United States. ‘the Usonian city’
‘Only in freedom can we build the Usonian city.’
A native or inhabitant of the United States.
‘we love life, we Usonians’
‘She is one of the second generation Usonians who moved back with her own family eight years ago.’
‘Forty per cent of Usonians speak Spanish as a native language, not to mention the many who speak it as a second language.’
Wiktionary defines Usonian similarly to Lexico, with no indication that the sense of "American" is obsolete, or even particularly formal or literary.
This seemed suspicious, as the first and only time I had heard the term "Usonia" was in association with the idealistic vision of Frank Lloyd Wright. Indeed, when I googled "usonia OR usonian -wright", basically all the results were some companies named Usonia or related to housing. The one exception I found was a single Reddit post:
I’m trying to find a video that I watched a while ago that was about the differences in British and Usonian English, I believe that the speaker was never shown and had a British accent. At one point he talks about biscuits, scones, and cookies where he remarked that British people exclaim "oh my god, biscuits and gravy‽".
(The use of the interrobang suggests the author is more willing to dabble in quirky language than most people.)
If it is obsolete, when did it become obsolete? Was there ever a time it was used as an ordinary, neutral term for American?