And, the subject of secession was not resolved... only in the sense of the “winner” of the war by act of force. Legally, it is still there for us.
Constitutionally:
TX, HI, VT and CA as sovereign entities before their acquisition to the US, can leave unilaterally. No vote necessary. If the state legislature were to pass a secession bill, they could leave.
GA, SC, NC, VA, PA, DE, MD, NY, NJ, MA, CT, RI and NH, as the original 13 colonies, could vote either as a whole or in part to leave. Arguably, with a majority this would mean the dissolution of the US. The following would then occur with a majority:
TN would have to compensate the state of North Carolina. MS and AL would have to compensate Georgia, for the central part, SC for the far northern strip, and the 13 for the Gulf coast. ME would have to compensate Massachusetts. WV, KY would have to compensate Virginia.
So they would have to reach agreement with these respective states.
Now, the remainder of the US states would also have to reach agreement with the original 13, either through a payment split 13 ways, to purchase claims from the 13 or through mutual agreement. These individual states could then decide either to remain independent, or to re-incorporate as the United States of America.
With a minority of the 13 leaving, they would split off unilaterally if they chose to go, and the remainder of the US would compensate them for their claims on their respective states. Say if Georgia alone were to leave, they would be compensated for the central portion of AL and MS.
This is part of the reason why the South was formed the way that it was, basically you had a vote of VA/GA/NC/SC going against the US, so only 4 of the 13. Had MD/DE gone, that would have been 6/13 which means that if one of PA/NY/NJ/CT/RI/MA or NH left, that the US would have dissolved. This is also why it was so important for Lincoln to keep MD and DE, because if they left he had to hang onto the other 7.