There is a very detailed privacy policy page on Telegram’s website, but it contains no mention of HIPAA or Business Associate Agreements.
The page briefly mentions how to submit GDPR-related queries and mentions secret chats, but it has no information about HIPAA compliance. Though security is a differentiator for Telegram, because of the lack of information about HIPAA on its site, users who need to collect PHI may want to explore using a different messaging app.