In this subchapter, “state agency” means:
(1) a department, commission, board, office, or other agency that is in the executive or legislative branch of state government and that was created by the constitution or a statute, including an institution of higher education as defined by § 61.003, Education Code; or
(2) the supreme court, the court of criminal appeals, a court of appeals, or the Texas Judicial Council or another agency in the judicial branch of state government.