I would continue to identify myself as "American" if USA broke up and each state became it's own country regardless of whether I went abroad prior to that or any other situation of that sort.
Some states that cause residents to have conversations like this:
Me: "I'm American. Freedom flavored." (don't make assumptions, anyone from North or South America is American)
You: "Cool, which state?"
Me: "A united state!"
You: "What in the actual fuck? They're all united. What specific state do you reside in and/or originate from? (Smartass...)"
Me: "Look... If you sweat all the small shit you're gonna die from a heart attack in your 50s."
You: "Holy shit... So... Florida?"
Me: "Worse."
You: "Ah... Question retracted."
This ignores that such a breaking up of the US would very likely be based on similar dynamics as "balkanizations" that see smaller groups put their own identidy above that of the bigger group.
Sentiments that will be reinforced during a civil war when these groups keep trading violence and atrocities with each other, that creates a lot of bad blood and tends to make people identify in ways that differentiate them from "the enemy".
Not even Americans are immune to that, it's an issue latent to this day whenever state rights vs federal government comes up.
Some states that cause residents to have conversations like this:
Me: "I'm American. Freedom flavored." (don't make assumptions, anyone from North or South America is American) You: "Cool, which state?" Me: "A united state!" You: "What in the actual fuck? They're all united. What specific state do you reside in and/or originate from? (Smartass...)" Me: "Look... If you sweat all the small shit you're gonna die from a heart attack in your 50s." You: "Holy shit... So... Florida?" Me: "Worse." You: "Ah... Question retracted."