My T is a complete blank slate -- to the point that even if I explicitly ask her something, she'll talk in general terms (E.g. about therapy / therapists) or deflect it back to me.

I am honestly comfortable with her doing it for these reasons -- about a decade ago, I had a T who shared a whole lot of herself. At that time, I was trying to come out as gay to my (ultra-conservative) family (in an ultra-conservative country) and that was sort of one of my biggest issues. The T I was seeing then totally dismissed my concerns about it -- she went into great detail about how she had an inter-racial marriage back in the 50s or something (I know it was a super big deal then) and her parents were totally cool. So, she kept telling me that my family would be totally fine too and I was underestimating my parents. Needless to say, she was dead wrong and it wouldn't have taken a genius to figure out that she'd be dead wrong -- I'd told her enough about my childhood and family for her to know that they had / have all kinds of issues with me and the gayness was / is just the icing on the cake, so to speak.

I didn't feel I could push back with that T though because she'd revealed a lot about herself (so, I also knew a ton about her family, vacations, likes / dislikes etc -- none of which I'd asked). So, it felt a lot more like a personal relationship and I felt that if I were to push back and ask for what I thought was 'better therapy', I'd be personally hurting her. Weird I know and I realize that I may be one of the few folk with this problem -- I'm tongue-tied when I have a professional + personal relationship with someone (so, I go to great lengths to avoid such relationships).

With my current T, I still hesitate to push back on stuff but not because I worry about the personal stuff -- it's more that she's a mistress of deflection and I usually think we'll go round and round in circles before I can get anything resembling a halfway satisfying answer from her. But, even in doing that, I feel much much much more comfortable because I don't feel like there's a "personal" component to our relationship and I don't care if she's hurt or whatever -- I figure she gets paid $$$ per hour and that's good enough (I mean I know she cares but I don't think it's my responsibility to worry how she feels).

I'm really sorry you're facing this issue with your T though -- for what it's worth, I totally understand your pain. My response is something that I sort of logically thought through knowing how I usually react to these things -- not sure if it'll help you.