How long term are we talking?
The war, debt, and slavery will wreck havoc for a long time. I can see the CSA falling apart. If they make it to the early 1900s though they will probably have diverged further from the North and have a stronger identity.
If it proves too unstable or fails to develop an identity then who knows? It could collapse into civil wars, rejoin the US, or fall under a totalitarian regime.
So if we assume they stay together, their white majority is fairly literate by global standards, has access to schools and nothing that really separates them from the rest of the international communities ideas. They have Capitalism and a history of transition of power. The slaves can do more than pick cotton and have been able to work in manufacturing at times. Slavery probably lasts into the 1900s and dies under international pressure in the early-mid 1900s.
I don’t think it ends up as rich as OTL, but don’t see it being poor if it survives. They have most of what’s needed for fast growth at some point in the future so even if they stagnate for a century, all it really takes is a few decades between 1950 and 2019 of good governance and GDP per head could go from $10,000 to $25,000 very quickly. And I don’t think that the CSA is removed enough from the rest of the world to go the entire 20th-21st century with dysfunctional economic policies. Looking at places in Southern Europe and East Asia that are below the confederacy in almost everything in 1860 but still developed eventually, I think the odds are in their favor that if they don’t implode they’ll eventually figure much of this stuff out.
I would expect them to have a white population that is still easily high income but unequal and led by a some kind of aristocracy that’s blended with new capitalists that have come along over a century and a half. The black population does much worse than the OTL for the next century after independence, but given that the last ~40 years of the OTL hasn’t seen much convergence between white and black Americans they might have time to catch up to their OTL counterparts by 2019, but are probably poorer than the OTL.
My scenario assumes the CSA is still alive, which is hardly inevitable even with a victory, so this means many of its worst case scenarios in its first few generations were avoided. So I overall think it is slightly to moderately poorer than the OTL today, probably somewhere between OTL Portugal or Greece and the OTL current Southern states economically, probably with all of the OTL Southern social dysfunction. But I don’t see them deviating that far from the rest of the Western and Anglo Worlds.