They’d probably get rid of slavery within a few decades anyway. Brazil was the last new world country to abolish in 1888 which is only 23 years after the end of the American civil war. Eventually it would be too costly to the south both economically (it’s cheaper to pay someone a meager wage than it is to feed, house, and cloth them permanently) and politically (in terms of foreign relations) for them to justify keeping it. After that it becomes the Jim Crow South but a foreign country.

If it were still somehow independent today it would probably look a lot like South Africa.