But outside it’s a very different story especially in places where the language isn’t English.

What is the demonym for something that can be found or belongs to “The Americas”, comprising both North and South America (and potentially Central if you go by the Three Americas way of splitting the continent)?

This is a fair question, and I suspect there simply is no generally accepted demonym in English. One could be introduced, but contrast that fairly simple exercise with the replacement of the broadly-recognized demonym for USA residents: “American”. Quickly, it becomes apparent that replacement is far harder than introducing a new demonym, even if the demonym itself isn’t very logical within the English language.

English is the same language that calls people from Deutschland as “German”, and then American English specifically might also call them “Dutch”, as in, the Pennsylvania Dutch, whom immigrated from Germany. Consistency is not strong in the English language, even over only a few hundred years.