What I’m wondering with this scenario is if the US might seek to reabsorb this new Texas republic provided they successfully break off from the CS.
I think Texas would have little interest in rejoining USA in this case. This hypothetical Texas rebel because its economy has shifted to oil and cattle, it has a BOP surplus and a foreign protector. There's little reason to rejoin USA, neither for the elite or the common people who either descend from people fighting USA or European immigrants. This is not the thinly populated Texas of the 1840ties which was an economic basket case.