Though I'd be careful about copy pasting this to the ATL, because the end of slavery, devastation of the war, and the boll weevil led to a diversification of the economy.
I certainly wouldn't copy-paste the OTL's South onto an independent Confederacy, but it gives us ballpark for estimating. If the Confederacy did as well as OTL's South, then on the eve of OTL's Great War, their manufacturing would narrowly edge out Italy, be roughly 2/3rds of Austria-Hungary's output, and a little under half of France's output.
I've seen posters claim that the independent Confederacy would be much more prosperous and industrialized than OTL's South, but that seems to be wishful thinking.
An independent Confederacy is very unlikely to do as well as OTL's former Confederate states. The Confederacy would have a weaker currency, higher inflation, larger public debt, lower population, lower education, lower protection of native industries, inferior infrastructure, and almost certainly less territory than OTL's South of 1913.
The Confederacy had a weaker currency than the US dollar, due to a complete lack of specie to back the currency. The Confederacy's currency reform did drop their inflation from a calamitous 700% to a merely ruinous 50%, but their inflation soon spiraled even higher as they continued to fund their government by massive deficit spending. By the end of the war, the
per capita Confederate debt was massively higher than the Union per capita debt. A lot of that debt came from Confederate "greybacks', many of which were redeemable with interest between 6 months and 2 years after the end of the war.
An independent Confederate population would be significantly lower than in OTL for several reasons. Roughly 1/7th of the slave population fled to the Union in OTL - none of them would voluntarily return.
Lincoln's Loyalists calculates that roughly 10% of draft age men from Confederate states served in the Union army - few if any of them would dare to return to an independent Confederacy. An independent Confederacy would also get less immigrants than OTL's postbellum South. Census records show that hardly any immigrants went to slave states. In 1860, immigrants were about 1/6th of the population of the Union states, but only about 1/40th the population of Confederate states.
An independent Confederacy would have lower education than OTL's South because it was illegal to teach blacks and a lot of Confederate leaders opposed public schooling as another form of "internal improvements". In OTL, a lot of the "carpetbaggers" were teachers who went south to create schools for the freedmen and poor whites. They won't be creating those schools in an independent Confederacy.
An independent Confederacy would have less protection of native industries because they believed strongly in low tariffs. An independent Confederacy would have inferior infrastructure to OTLs South because their Constitution made it illegal for the government to fund "internal improvements". Southern railroads also wouldn't be getting the level of investment or standardization from northern financiers that they did in OTL.
The Confederacy will also probably be smaller than the 11 states that seceded in OTL. Not even Robert E Lee could keep the Union from getting West Virginia. Unless the Confederacy can produce at least one general who exceeds Lee in skill, they will at a minimum also lose some or all of Arkansas and Tennessee, and they could lose quite a bit more.