In "The Defector," Picard refers to George Custer as a "countryman" of Riker's. So the USA does still exist as a country, Alaska is still apart of it, and Will Riker is the same nationality as Custer ... American.
Or the "country" in question could be North Am(erica), which includes but is not limited to the former United States. After all, Alaska wasn't a part of the US until just 62 years ago. Countries can grow or combine with other countries.
Now, in "Lower Decks" we did have Riker correcting Sam Lavelle when the latter thought Riker was Canadian. But that could just be like what happened to me at Shore Leave recently when someone thought I was from New York and I told them no, I'm from Cincinnati. Just pointing out the difference doesn't mean they aren't part of the same geopolitical entity.