She answered your question - you say that you asked if she had been busy, and she replied that she had. What if she had ignored your question? That would probably not have felt good, either.

I wonder if there is still an element here of your not liking the fact that we are our therapist's jobs. Your T was busy with other work instead of prioritising the part of her job that involves replying to your email. Do you think that might be part of it?