OP, I have to say that all sounds pretty awful.
A therapeutic hour, as it's called, is 50 minutes. I've never heard of a session only lasting 30 minutes from start to finish.
As for interrupting you. Part of the therapist's skill is to pace the session. This includes preparing for the end, so that the client can leave "zipped up", ie ready to resume their day to day life after what is usually quite a full on experience. If she is asking whether she can interrupt you that's not good.
When you spoke about how your anxiety presents and the triggers, to say we're not talking about that now. Well, that's just plain awful. Despite CBT not being overly concerned with exploring past trauma etc in detail, the therapist should still be seeking to build the therapeutic relationship. It's a collaborative, collegiate approach. To cut you down like that, at the beginning, especially when you were talking about what will be the core issues is really bad. I wonder when she was planning on exploring those issues with you?!
Although it's getting better, counselling is quite poorly regulated, and training standards differ widely. I think you'd be well advised to go in next week with a list of questions you want to ask. Show her you're well informed, ready to engage, and that you want to start the work. If there's no improvement, go over her head and say you'd like to be referred to a more experienced therapist, as this one seems unable to meet your needs.
Her supervisor will start to see a pattern of DNA, "did not attend", after a while, and action should be taken. But in the meantime people like you will be badly let down just when you most need support.