You're treating two different documents that were written 14 years apart by two diffent, though strongly overlapping, groups of people as if they were statements someone made back to back. Did Thomas Jefferson believe the words "All Men" included the slaves he owned when he penned those words? Fuck no! But he still wrote the words in a way that men who did believe that "All Men" meant ALL men could get behind it. Compare this to how he describes the Natives.
"He has excited domestic insurrections amongst us, and has endeavoured to bring on the inhabitants of our frontiers, the merciless Indian Savages, whose known rule of warfare, is an undistinguished destruction of all ages, sexes and conditions."
By examining the nuance, you can start to see a fuller shape of the society. Slavery was a hot button issue that was left unspoken until the moment it unquestionably has to be addressed. The Native Americans are considered savage and warlike, and that is an uncontroversial view.
I understand the impulse to fight back against whitewashed history, but throwing out all nuance isn't helpful no matter what cause it is in service to.
That said the “State power” argument in this case has always been the justification for the treason committed by the confederacy. When faced with a legally elected president, making a legal change that they didn’t like, the confederate states mutinied.
They have retroactively tried to call it the “war of northern aggression” (hint, you committed treason, so it’s not). Then they’ve claimed it was about states rights - if it was, then the Supreme Court would have ruled it unconstitutional, they’ve also never mutinied over anything else.