I agree that this is a common and pretty low-stakes question. However, I don't think my T has ever actually answered it (he's also not big on self-disclosure, but has become more open since the pandemic). Maybe it's a case where the T has their own mental health issues that they don't want to disclose? Or that a parent or sibling does/did? If it's just "I like helping people," or "my friends have always said I'm a good listener and very understanding," then I'd think they'd be open to sharing.

To answer your question, I have had similar issues with my T not responding to what I thought were fairly basic questions, and we worked through it, generally by talking about it, or else my deciding it wasn't important enough to make a big thing out of it. It should be OK for you to ask anything--the T just has the option to not answer. I'd try talking about it with your T, difficult though it may seem.