I would feel hurt too. He is there but he isn't there. I don't think that ts should promise they can be there because realistically no one can promise that. It sounds like he is really trying to be there for you, offering iahip support over the phone if you wanted it.
What was it you did want from him out of curiosity? Different people want different things. I have often text t in a crisis. She will sometimes text back day after or sometimes that day and sometimes it's enough just to hear her voice or see her text. I just need a little reassurance that someone heard I am in distress. Is that enough for you or do you need something else. I see you have talked about his lack of response but it could be useful to talk about what you need from him when he does respond as often ts don't know and often upset the client more with their lack of response!
It could be worth looking at this again with your t, he seems very open to helping you whatever way you need.