I tried writing a novel, much like Jeff Brooks did years ago. So I have my own little thoughts of how things would have looked.
What happened in our timeline was the boll weevil came in during the high point of the cotton barons in the 1890s. Confederate adventurism in Mexico could lead to the weevil being introduced a decade earlier. Now, since in the CSA, the infrastructure of the Deep South is still well intact and never saw the scorched earth of 1864-65. It causes a situation similar to real life where the money leaves the Mississippi Delta, Black Belt, Alabama Wiregrass regions and such that subsisted off cotton for decades. Blacks are de-facto freed and take to the countryside, uneducated, a manumission amendment is eventually passed at the turn of the century, and a new apartheid-type system takes it's place by 1910. Strict yes, but more paternal than post-Civil War reactionary. It'll be a forced economic diversification. And the Confederacy will become an economic colony of American, French and British financial interests, with light steel and coal industry popping up in the Upper South, North Georgia and North Alabama. Virginia becomes the CSA's most populous state, New Orleans is 2 or 3 times the size it is in real life, and Atlanta still becomes a major communications hub for the country. Brazil abolishes slavery around the same time.
Texas probably becomes autonomous later on more than likely.
For the Union, there is no Texas v. White, it's basically been established by blood that a state CAN leave the Union. And the next candidate to go is definitely going to be Utah.