Let's go with abolished peacefully eventually with compensated emancipation for the slaveholder?
This is a fun experiment.
OTL blacks tended to stay in the South for a while after the Civil War, for a few reasons: it was the only home they knew, their families and friends were there, and they had the numbers to build a community. The one-two combo of extreme racial violence and the booming economy in the North convinced many blacks that leaving their homes and families (usually with the goal of bringing them up North after jobs were secured) was worth it for employment and a fair(er) shot at making it.
TTL, the one-two combo is in doubt. Assuming a peaceful abolition, the Southern economy would not be so utterly devastated as it was post-Civil War. Adding on to that compensated emancipation, and the South now has actual capital to invest in industry and infrastructure. Whether they use it for that is another matter, but lets assume they do. In TTL, the South, while certainly not as economically strong as the North, would at least start on a better base than it did OTL, which might provide more economic opportunity than blacks found OTL.
The second issue, racial suppression, probably isn't going to go away. However, it cannot be overstated how much of the South's racial violence was due to the suddenness of emancipation
and the shame of defeat. Southerners, utterly broken, clung on to the one power source they had left after the war: white power. TTL, emancipation is gradual, peaceful, and expected, meaning people have more time to adapt. Will this butterfly racism? No. But it might lessen the brutality of it compared to OTL.
All of these things, in addition to OTL familial and social ties,
might convince more blacks to stay in the South compared to OTL, which may mean that blacks stay a majority in many Southern states for longer. It would also mean a larger and overall richer (depending on the South's policies) Southern society.
There's also the issue of millions more men being alive and not physically/mentally scared, of course.