The US Constitution does not prohibited secession either. The US Constitution is silent on the issue. You stand corrected.
Any constitution or republic that made provision for its own dissolution and destruction wouldn’t be much of a constitution.
Of course, our Constitution does make provision for lawful, peaceful, constitutional changes if you’ve got a gripe.
The original colonies, and Texas, could present a facially legitimate argument that they had a right to seceed. States admitted to the Union after the ratification of the Constitution were created by the Union. Having never been independent polities prior to statehood, I don’t believe there is any legitmate argument they could make that they had a right to seceed from the nation that created them.