Would you call South Asian laborers who are temporarily working in construction in Dubai expats? Seems to fit your definition exactly.
Expats have a great deal more agency about their lives: where they live, where they work, when to return, etc.
To be clear, I don't particularly like this distinction, but it absolutely is a thing in the Middle East down to separate immigration lines at airports, and if anything glossing it over by calling the Bangladeshi construction worker living in a container in the brutal heat and sharing a latrine with 50 other guys an "expat" does nobody any favors. Or was the American South powered by African "expat" labor too?