Consumer protection law: Texas Deceptive Trade Practices-Consumer Protection Act (Tex. Bus. & Com. Code section 17.41 et seq.). It applies to businesses generally, not to chatbots specifically; whether it reaches a particular chatbot practice is a legal question.
Consumer privacy law: Texas Data Privacy and Security Act (Tex. Bus. & Com. Code ch. 541 (section 541.001 et seq.)), in effect from July 1, 2024. It sets rules for personal data, which can include what people type into a chatbot, for businesses that meet its thresholds.