The great majority of Texans feel they are citizens of both the United States and the State of Texas.
I bet a majority of the citizens of most states feel the same way.
Your conjecturing of the beliefs of people is getting way over the top.
While that may be what we have today, recall that Robert E. Lee, having been offered command of the Federal Army of the Potomac, declined and went back to his native Virginia to take command of troops there. Lee was a Virginian first, as were many folks in those days, ordering their primary loyalty to their State.
Those States had armies, and the Armies of Pennsylvania and Massachusetts invaded the State of my ancestors, that State remaining occupied through the war.
Regardless of which side they fought on, the regiments were not known as "the Federal Army" so much as the 1st Wisconsin, 2nd New York, or on the other side, the 1st Virginia, 1st Maryland Volunteers, etc.
This was before the 17th Amendment when the State Legislatures still elected the Senate, and State Government had far more power since usurped by the Federal Government.
Trying to measure original intent by the pap that passes for "government class" (not even civics) today, and the creeping totalitarianism of the past 100+ years is silly. You won't get there. Study the attitudes of the people when the concepts were still fresh. Then examine the economic reasons for the war to retain the South by force.