My general point is that the precedents of the Supreme Court, unlike any other court, are by definition binding on any court in the land, because any court's decision, ultimately, can be appealed to the Supreme Court. This isn't the case with any other federal court. A District Court's opinion, therefore, on state law cases can be outright ignored by a state court. It has no binding precedential authority.EDIT: I suppose it seems worth repeating; It doesn't look like any of us are actually disagreeing with each other (aside from potentially the minor disagreement on application of Erie). I made a point of clarification for informational purposes because this thread is also populated by users who have a less firm understanding of how binding authority works in State vs Fed level.
The decision of the Supreme Court would be binding on the Texas Supreme Court and its own inferior courts, because it can be appealed there. You aren't going to see many decisions on state law because its appellate jurisdiction doesn't allow it to rule on state court interpretations of state law with no contradiction with federal or U.S. constitutional law. If you did, though, possibly through an exercise of the Court's original (as opposed to appellate) jurisdiction, it would still be applicable.
Specifically, though, Article III provides: "In all other Cases before mentioned, the Supreme Court shall have appellate Jurisdiction, both as to Law and Fact, with such Exceptions, and under such Regulations as the Congress shall make." Even SCOTUS could overrule a state court decision on state law based on fact, at least within its constitutional limits (Congress can limit its appellate but not original jurisdiction). This is vastly limited in jury cases by the Seventh Amendment but that's a different issue.