Key tones, for me it seems like a red flag that the therapist insisted on hearing your reaction to her disclosing about her major depression. The therapy session should be focussed on you. How can your reaction to her disclosure be relevant? It makes it sound as if she is trying to use the session to focus on herself, and that is really inappropriate.

Some Ts are careful not to disclose anything at all about themselves. Personally I would find those Ts difficult to work with. My T self-discloses quite a lot about little things, and it helps me to trust him and for us to have a good therepeutic relationship. But I don't think he would disclose about a problem with his own mental health because that would lead to me focussing on him and maybe feeling worried around him or worrying that he couldn't cope with my therapy. And he certainly never insists on me reacting to any disclosure of his. If I ignore it then we move on.

I don't want to say "you must leave this T" because that's up to you of course and also you know the context, and whether this T really helping you overall. I will just say that if this happened to me with a T I had only been seeing for a short while, I would definitely consider trying out other Ts with a view to leaving for a new T.