Nope, no tendrils. It has a loose climbing habit but doesn’t grasp tightly, and in fact is zip-tied to the post. I’d liken it to tomatoes - they WANT to climb but end up sprawling, bless their little nightshade hearts.
It looks to me like Radermachera sinica, also known as China Doll. It’s generally sold as a houseplant, but I could see it preferring the outdoors in Texas, as long as it doesn’t freeze.
That one gets my vote as well. It’s a ubiquitous houseplant whose popularity puzzles me, since it’s plain-looking and doesn’t flower (indoors, anyway).