Pretty sure I know an org that has baa with OpenAI directly. Agree that azure is more straightforward (and what I did at my startup).
It’s probably a lot easier if you’re a corp with name recognition, but the regular folks who post online about it have said no luck so far.
Not hi-trust afaik, but they will do hipaa eligible baa with select customers. As sister comment says, it’s easier to go through azure and you get basically the gamut of azure compliance certs for free.