I see a lot of good and reasonable discussion here, and I can understand why it's a topic for discussion even among therapists.

I do think though that it is wise to keep this in context: ie, that you've (rainbow) worked a lot on attachment issues with your therapist and specifically she refused to give the requested information about her boyfriend, setting a boundary, and sort of shut you down from talking fully about what impact that had on you. And now you are dealing with a compulsion or obsession surrounding finding information about him. It was not just an idle curiosity that this particular wanting to research therapist's boyfriend but was in direct relation to what went on in those sessions and after the therapist declined to provide the information. This sounds like a lot of "old stuff" getting dragged up just imho. Do you struggle with feeling shut out of your family, or something similar?

I hope that you're able to find what it is you're really looking for, because something tells me it's not just a picture of her boyfriend.