I'd give my T the benefit of the doubt about the knowing thing; I "know" my neighbors, smile, wave, and even talk to them but couldn't tell you their names so if you asked me do I know "Sam Spam" I might say no since I don't know anyone by that name but if you showed me a picture and asked, "do you know this person" my answer would be different. It is one thing for your friend to know who she is if you have discussed her, her name, where she lives, etc., because then your friend knows you are talking about the woman 4 houses up in the purple house whereas your T hasn't been discussing your friend with you so doesn't know she is the woman 4 houses down in the green house

If she really did know my ex-gf and knew that's who I was talking to/about/etc. she could have been feeling like she was skating on thin ice with a conflict of interest, seeing you and knowing her at the same time or that it might spook you, etc. and she obviously likes seeing you and would not want to mess that up with, "Oh, I know your ex-gf, I can't talk about her whether she's important to you or not and/or can't see you anymore because I can't be unbiased enough," etc.

That she is your ex-T's supervisor is a work thing and their business, not yours. Your ex-T may/may not have discussed you but did not use your name or identify you as such and your present T cannot know that your ex-T identified her as her supervisor to you unless you said, "Hey, you're ex-T's supervisor aren't you?" I don't think she'd say, "No, I don't know what you're talking about" to that direct question?