Does the Constitution actually prohibit a state from leaving?

No. There is no clause in the United States Constitution that forbids a state from leaving the union. Read the document from the Preamble to the Twenty-seventh Amendment and you will not find the prohibition, because it is not there.

The Constitution is a list of powers, and this one is not on the list

The federal Constitution works by enumeration. Article I, Section 8 lists what the federal Congress is allowed to do: coin money, raise armies, regulate commerce, establish post offices, and so on down a finite list. If a power is not granted, the federal government does not have it. There is no "power to prohibit a state from leaving" anywhere in that list, and there is no "power to hold the union together by force." The thing opponents insist the federal government possesses was never handed to it.

Article I, Section 10 is the actual list of what states cannot do, and leaving is not on it either

The Framers knew exactly how to restrict the states when they wanted to. Article I, Section 10 is a precise catalog of the things states are forbidden to do: enter treaties, coin money, pass bills of attainder, lay tariffs without the consent of Congress, keep troops in peacetime, make compacts with foreign powers, or engage in war unless actually invaded. The Framers sat down and wrote out the limits on state power line by line. Leaving the union is absent from that list. When the people drafting a document specify what is prohibited and leave something out, the omission is not an accident. It is a decision.

Silence, in a system of enumerated powers, is not a gap. It is an answer.

This is the heart of it. In a government of enumerated powers, what the document does not grant is not delegated, and what is not delegated is not a federal power at all. The lawyers have a Latin phrase for the interpretive rule, expressio unius est exclusio alterius: to express one thing is to exclude the others. Francis Bacon put the same idea plainly centuries ago. As he wrote, "As exception strengthens the force of a law in cases not excepted; so enumeration weakens it, in cases not enumerated." The Framers enumerated the limits on the states. Leaving was not among them. The silence is the answer.

The strongest version of the argument is not "the text permits it." It is "the power to stop it was never granted."

We are not claiming the Constitution contains a clause that expressly authorizes a state to leave. We are pointing out something more durable. In a system built on enumerated powers, the federal government can only do what it was empowered to do, and it was never empowered to prevent a state from leaving. That is not a loophole. That is the design. The burden is not on Texas to find permission. The burden is on Washington to find the power, and the power is not in the document.

This was the understanding of the founding generation

The view that powers not surrendered remained with the states was not a fringe position. It was the mainstream understanding of how the Constitution worked. St. George Tucker, whose 1803 edition of Blackstone's Commentaries was the first major legal treatise on the new Constitution, described each state as remaining "a perfect state, still sovereign, still independent, and still capable, should the occasion require, to resume the exercise of its functions." The idea that joining the union dissolved the states into a single consolidated mass came later, and it had to be argued for against the plain understanding of the people who ratified the thing.

The bottom line

The Constitution does not prohibit a state from leaving the union, because the power to stop it was never given to the federal government in the first place. The argument against Texas independence has always been a political argument dressed up as a legal one. On the law, the door was never locked.