It simply isn't true that nobody thought that secession was unconstitutional before Lincoln. James Buchanan said as much in his December 1860 State of the Union message.
According to Buchanan, unilateral secession was only justified as a revolutionary act of resistance to tyranny, and not under any other circumstances. That was a widespread understanding at the time.
Since the US wasn't a tyranny in 1860 unilateral state secession was unconstitutional. Buchanan, though, didn't think the federal government could do anything about this unconstitutional act.
There was a widespread understanding in 1861 that the country was faced with a revolutionary situation. This affected Lincoln's thinking and actions, and Davis's as well. Davis and other secessionists were acting outside and against the law more than Lincoln was.
"Since the US wasn't a tyranny in 1860 unilateral state secession was unconstitutional."
Oh really? Since the Constitution is silent on the matter I don't know how you or anyone can make such a bold statement!
"Buchanan, though, didn't think the federal government could do anything about this unconstitutional act."
That's because it clearly wasn't unconstitutional and was a right reserved to the states by the 10th Amendment within the Bill of Rights!
What did this have to do with our debate? Why should I care what Davis was up to?