No. There are no teachers unions in Texas. There are teacher organizations, but no unions. [Trust me, I know about this, because I belonged to ATPE.] Membership is high in teacher organizations because that’s how a teacher gets professional insurance and has access to lawyers for professional concerns. You are correct that these organizations have little power beyond, for instance, helping a teacher hold a principal or school district to the law. One of these organizations cannot save a teacher from being justifiably released or fired.
“[Trust me, I know about this, because I belonged to ATPE.”
That org. was mostly for the legal services wasn’t it.