And no consensus that it didn't. It took the Supreme Court to rule after the rebellion was over that secession without the consent of the states was not supported by the Constitution.
As if they would rule any other way. I think secession was fool hardy and wrong for several reasons. I don’t think it was illegal at the time. We will never know whether Lincoln would have called up troops if Fort Sumter had not been fired upon. Once that happened the U.S. government was justified in going to war against the Confederacy.
My point is that those who fought for the Confederacy were not traitors. Even if after the war the secession was found to be illegal when they enlisted in the Confederate military they believed they were fighting on behalf of a separate country and not making war on their own nation.