Ah, indeed, it's more clear. In summary, there should be another name than "British Isles" to describe that archipelago. Interestingly enough, it seems like schools books in Ireland indeed do that

In October 2006, Irish educational publisher Folens announced that it was removing the term from its popular school atlas effective in January 2007.

'The British Isles' has a dated ring to it, as if we are still part of the Empire".

Writing in The Irish Times in 2016, Donald Clarke described the term as "anachronistically named"

A bilingual dictionary website maintained by Foras na Gaeilge translates "British Isles" into Irish as Éire agus an Bhreatain Mhór "Ireland and Great Britain"

https://en.wikipedia.org/wiki/Names_of_the_British_Isles#Republic_of_Ireland

So, if we were to use this logic for the USA, there may be another demonym to use? Spanish has “Estadounidense” (https://dle.rae.es/estadounidense), which in English would be something like UnitedStatesian, or USian