Article I Section 10 of the US Constitution prohibits states from negotiating trade agreements, declaring war, or conducting diplomacy because these are powers granted to the Federal Government. That makes it pretty clear that states are not sovereign nations. If they cannot negotiate their own treaties or trade deals, they certainly don't have the power to leave the union at will. If such a right existed in the US Constitution, there would never have been a US Civil War.
Go back to the basic meanings of the words; granted, delegated. Delegated powers can be recovered by the that which delegates. If you hire someone to manage your business you delegate certain powers of your ownership to that manager. If he does a poor job you fire that manager and reassume those powers.
That means that the states have these powers and as part of the compact that is the Constitution the states delegate these powers to the entity that the states created that is the federal government.
The states created the federal government and they can uncreate it or leave it at will. The states would never have joined the union if they thought that they could not leave it if the so desired. They had just fought an eight-yearlong bloody war to escape the tyranny of Great Britain. They were not about to voluntarily enter a new potentially tyrannical union without the knowing that they could exit should it to become despotic.
Again, look to the meaning of words. The word ‘state’ itself means a sovereign political entity. The name ‘United States’ means a group of sovereign states voluntarily joined together to form a confederation of states for their mutual benefit. As a sovereign state they can voluntarily exit that union at their choosing.
The Civil War is no proof of your assertion. Lincoln’s cause for war was the attack on Fort Sumter. Lincoln was negotiating to keep the Confederate States in the Union until that point.