If he’s still the AG, I wonder if he has any right to be on the floor of the House at all. That may be the issue.
According to another article, “While access to the floor of the House is limited when business is being conducted, statewide officials and former members of the Texas House—of which Paxton is both—are regularly granted access.”
https://texasscorecard.com/state/speaker-dade-phelan-removes-ken-paxton-from-the-house-chamber/