Well, no. The Civil War was not fought over slavery. Economics: Northern mercantilism. Slavery was already becoming uneconomical (cotton prices, corn the new cash crop) Lincoln freeing the slaves was an after thought—and he only freed the slaves in southern states. Missouri? U.S. Grant? Had slaves.
Have seen this repeated before, that getting rid of slavery was an afterthought. So I did a little research. It shows comprehensively that the hemming in and then destruction of slavery was a continuous process from May of 1861 (the month after the war started) to December of 1865, when it finally triumphed.
1861
May: General Butler refuses to return three slaves being used to build CSA fortifications to their owner.
Concept of “contraband of war” originated.
August: Confiscation Act of 1861 declares that any property, including slaves, used by CSA could be confiscated by military action.
September: “Contrabands” employed by US Army and Navy paid wages, in addition to rations
November: Nathaniel Gordon (a Mainer) convicted and sentenced to death in NYC for slave trading (classified as piracy)
1862
February: Nathaniel Gordon executed
March: Washington, DC slaves freed by Congress
Return of escaped slaves to their owners prohibited by Congress
April: Congress offers compensation to any state that emancipates
May: Lincoln publicly urges border states to free slaves
Slavery prohibited in territories
July: Lincoln appeals again to the border states
September: Preliminary Emancipation Proclamation
1863
January: Final Emancipation Proclamation
July: WV slaves freed by state action
1864
January: 13th Amendment introduced
March: AR slaves freed by state action
April: 13th Amendment passes Senate
June: Congress repeals Fugitive Slave Law
September: LA slaves freed by state action
November: MD slaves freed by state action
1865
January: MO slaves freed by state action
13th Amendment passes House
February: TN slaves freed by state action
April: Lee surrenders
December: 13th Amendment ratified
Slaves in KY (50,000) and DE (200) freed
Notably, as you can see, Missouri slaves were freed by state action, not by the 13th Amendment.
As far as cotton becoming uneconomical, that is no doubt why slave prices reached their all-time high in 1860. Wise businessmen always bid up the price of a commodity when it is losing its market. /sarc