It's not a yes/no question. We live in a more complex world than can't be simply digitalized into either/or choices, but then you recognized that with your hybrid option tilting the vote .
In the larger scheme of things, he was the catalyst that started the events eventually leading to the 13th Amendment which actually abolished slavery or involuntary servitude (except for convicted prisoners) after Lincoln's death.
He usually is credited for ending slavery with the Emancipation Proclamation, but it only applied to Confederate States and he only issued it after significant portions of the territory in the Confederate States already were under the control of Union soldiers in hopes of promoting slaves to revolt and join the Union military effort. It did not affect slavery in border states that still permitted slavery but had opted to stay in the Union.
And the myth of him being a shining white knight who ran for President to free the slaves, and did so, is largely just that: myth. The big issue in his election was not ending slavery where it existed, but to exclude it from new territories and states. His actual solution to existing slavery was for states to voluntarily abolish slavery as they recognized it was an unsustainable economic system, compensating slave owners for the loss of their "property", and providing free transit for slaves back to Africa for those wanting it. When the Confederate States seceded, the driving issue for him was maintaining the Union, not ending slavery.
And as you pointed out in your third option, slavery still exists in many different forms world-wide including in the U.S.; it is just not legal in most countries.
But the quick answer is, events moved him to be the poster child of the abolitionist movement although he was never the most forceful advocate of such, and his successful leadership in winning the Civil War led to the abolishment of legal slave ownership. The route to that point became, as usual with politics, the art of the possible at any given moment.