> Do these people also believe in a single continent called “Eurasia”?
It's the traditional six-continent model (America, Africa, Europe, Asia, Australia, Antarctica), which according to https://pt.wikipedia.org/wiki/Continente is the model taught in school in many places, including Italy, Spain, Portugal, and all over Latin America. So no, "these people" (which includes nearly all of America outside the USA and Canada) have learned about Europe and Asia as two separate continents.
On the other hand, the seven‐continent model is dominant in the Anglosphere. So it seems the sensible thing to do is what in fact is already normally done: in Spanish and other such languages, use “América” to refer to North and South America, and in English, use “America” to refer to the USA and “the Americas” to refer to North and South America.
It's the traditional six-continent model (America, Africa, Europe, Asia, Australia, Antarctica), which according to https://pt.wikipedia.org/wiki/Continente is the model taught in school in many places, including Italy, Spain, Portugal, and all over Latin America. So no, "these people" (which includes nearly all of America outside the USA and Canada) have learned about Europe and Asia as two separate continents.