I don't even know how I fell down this rabbit hole.
Texas does not have a state beverage. Some claim it has an unofficial state drink, which is the margarita.
The margarita was invented in El Paso, Texas by a Mexican truck driver (yeah, I don't know how that happens either). The first appearance of the drink was reportedly at a bar called "Tommy's Place" in 1942.
Now onto "beverages" because I guess "drinks" denote a mixed drink or something. If one was really looking to promote the state of Texas and its accomplishments, then someone should step up and nominate Dr. Pepper as the state beverage. Dr. Pepper was invented in Waco in 1886 (a year before Coca-Cola was introduced for those who didn't notice).
Although the margarita and Dr.Pepper are pretty darn notable for being invented here, I still don't think they're the "state drink/beverage". For me, the connotation should mean the most popular drink, and while both are popular, they're low profile compared to my selection.
The rub is this, when something becomes the "state ____" it's actually political. It's that state looking to promote something for trade or image purposes. In fact, "milk" is the state beverage for over twenty states, either to portray a wholesome image, to promote dairy products, or because they were lobbied to by milk producers.
So let's get to it. What should the state beverage of Texas be? You already know the answer. I'm going with sweet tea. Now since Texas doesn't produce tea (as I know it) I doubt it will ever be official, but if you see two people sipping on some cold drinks on a porch or in a restaurant, it's usually sweet tea.