Not sure why you would think seceding from the union would be unconstitutional? ALL States are sovereign, having their own constitution, so to speak. Joining the 'union' which is the 'United States" is all voluntary. Each is free to govern in its own way by their own laws. Which is why the current president is insistent that they each lead their own in this virus fight.
It is illegal, and was so during the civil war.
Texplainer: If Brexit Can Happen, Can Texit?
"In the 1869 case Texas v. White, the Court held that individual states could not unilaterally secede from the Union and that the acts of the insurgent Texas Legislature — even if ratified by a majority of Texans — were "absolutely null."
If there were any doubt remaining after that, late Supreme Court Justice Antonin Scalia set it to rest more than a century later with his response to a letter from a screenwriter in 2006 asking if there is a legal basis for secession.
“The answer is clear,” Scalia wrote. “If there was any constitutional issue resolved by the Civil War, it is that there is no right to secede"
So Texas (or any other state) cannot legally secede. However, Texas does have one option that other states do not. It can divide into 5 separate states. This is because, unlike other states, it was never a colony or a territory, but an independent nation and joined by treaty.