An immigrant joins a country

An emigrant leaves a country

OP doesn't know where they're going, just that they're leaving a country. Because of that "potential emigrant" is the pedantically correct term for now.

When/if OP enters another country, he would be an immigrant to that country and an emigrant from the US.

They say "expat" in new country because they don't want to call themselves immigrants searching for a better life, even when they're open about that being what they're doing. And they get to keep "US" in front of it which is a huge bonus for some people despite America's reputation.

But once over there when talking to people also over there, they should be identifying as an immigrant.

Doing anything else, is only going to make friends with other "US expats" like the boomer communities in Mexico where no one speaks Spanish and they put zero effort into fitting in. Wherever you go that paints a target on your back, not just for outright crime, but to get taken advantage of by locals at every opportunity.

Ironically they're often liable to keep complaining about how immigrants don't try to integrate in America, even after leaving.

They just want to live somewhere that they're "rich" compared to everyone else.