Leaving slavery out of it, the confederacy never would have been strong enough to support a war. How does the south build itself up into something strong with labor that they had to pay for?
Or a state would have tried it, there would have been a military response, and that state would have been crushed. Hypocritical? Sure. But George Washington put down the Whiskey Rebellion, so, you know.
It’s one giant sunk cost fallacy, pretty much. If all your wealth is tied up in slaves, how do you liquidate their for anywhere near their value?
Harry Turtledove has made a large chunk of his writing career answering that question. The CSA wins the war because Lee’s Special Order 191 was recovered instead of being lost. Without that intelligence, McClellan badly loses the Battle of Antietam instead of forcing the Army of Northern Virginia to withdraw, which encourages Great Britain and France to recognize the new country. Among other things, pressured by GB and France, the CSA has a slow manumission of its slaves, completed in the 1880s (not that the former slaves’ lives improved much) and when The Great War erupts, the USA aligns itself with the Central Powers and the CSA with the Entente.
The eleven book series continues on to conclude in 1945 at the end of The Great War II.
In addition, his standalone novel, Guns of the South, has time travelers supplying Lee’s army with AK-47s and other materiel in January, 1864 which allows it to prevail over the Federal armies and leads to a Southern victory. The scope of the book is much less than the series ending in 1868 whenthe CSA realizes the time travelers do not have the new nation’s best interests at heart and drives them out of their enclave, destroying the time machine in the process.
Not written here, but Utah could have jumped ship had the CSA won. Brigham Young had already fought the Utah War in 1857 to 1858 in order to attempt to remain a theocracy. While the Mormons backed down, had the Civil War gone differently then Young would have liked to had stuck it to the Feds. He and the other Mormon leaders detested the Federal government, holding them responsible for the murder of Joseph Smith.
The southerns parts of New Mexico and Arizona may have gone with the CSA, but the main prize California would probably remain with the US.
It would not have been two equals splitting the lower 48.
Oddly the Confederate constitution doesn’t forbid or allow secession, it seems to give a nod to it being possible but doesn’t explicitly say so. I think that is likely to be a major problem for both sides after a split, though oddly all of the fiction I can think of doesn’t have either the USA or CSA further fragmenting after it’s established that states can leave.
Also because a lot of rich and powerful people had a lot of their wealth tied up in owning slaves. Making them free would suddenly make a lot of politically influential people much less rich, so any plan to free the slaves would need to address that. The US didn’t have that problem post-civil-war because they could essentially say ‘you lost, suck it up buttercup’. The confederate constitution also explicitly protected slavery - states had to allow and protect the institution, and congress was absolutely forbidden from interfering with it. While the constitution could be amended, I don’t think it would be as simple as most fiction that has the Confederates ditching slavery a mere two decades after the was imply.