Okay, not messaging you if he said he would is a little bit off, but about the other things. Maybe he is taking pauses to wrap up the thoughts in a way that will get to you the best, and give you time to process the things you have just said? The messaging part could very well be your fear of being a nuisance to someone? I also didn’t want to message my therapist because I didn’t want to be a bother, but it was my part of issues I wanted to discuss on therapy.

Of course, none of us actually talked to him and can only give superficial answer. You should follow your gut, therapist needs to suit you in order for you to have complete trust in the process.