Many of us have therapists who always (or nearly always) wait for us to start the conversation and don't try to set the agenda for the session. My experience with my therapist, who is an extremely good T, is that he'll wait for me to start talking but then he'll help me along, ask questions, challenge me on points where he doesn't agree, and try to take the discussion to a deeper level than what I could do on my own. So it's a collaborative discussion, certainly not a matter of him deciding what we should talk about or steering the conversation, but also not just me talking and he listening and supporting me.

It's very common, I think, that a therapist takes a lot of notes during the first couple of sessions, when they don't know us at all and need to get all the practical details down.

What really raises a flag for me is that you see her as stern and cold. I don't think a therapist needs to be a warm and fuzzy teddybear (in fact I don't think that's a therapist's function at all) but they do have to display empathy and interest for the client.