All of the above is completely correct and I don't mean to disagree with it. I do mean however to point that there's something of an important difference between the demographic make-up and mentality of Texas pre and post annexation.
Pre-annexation Texas was still almot a bi-ethnic state, with a lot of Tejano influence (eg Juan Seguin). The right to keep Santa Anna from taking their slaves away was a big reason why Anglos supported the Texas Revolution, but not why the Tejano communities came around. Nevertheless, the Republic's constitution did enact protections for slavery (much like a Southern state did at the same time).
However, after annexation, Texas saw huges waves of white settlement which transformed whites into the dominant class / group. The lion's share of that settlement came from the South and increased the extent of slavery in the state (mostly because annexation proved a boon to the Texas economy, stablized the monetary and financial systems, and provided for security).
A Texas that isn't annexed probably won't see as much immigration from the Southern US. It may well see increased amounts of foreign immigrants (Germans, Irish) if the US goes more nativist and Texas becomes an easier haven. In any case, the differing demographic would mean that slavery might have a different future. That being said, Texas will hang on to slavery for quite a while, if it can. However, it will be even more at the mercy of potential British pressure for abolition than a surviving CSA (though of course the British might well not exert such pressure).
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