I do this kind of thing not only with therapists but as part of educational and business strategies in my work as well. I don't see anything dishonest in it, firstly because I can't see what can be wrong with looking at public online info of any kind, secondly because you just want to use those pieces of information and dive into it more deeply, use it for relationship building etc. It reminds me of reading someone's (stranger) interests on their website or an online profile, getting interested in them based on it, contacting them to explore it further. After all, I found both of my Ts online and got interested in them based on what they had to say about themselves on the web. I think actually asking them upfront without saying that you already know is more gentle and less intrusive than a statement along the lines of "I have seen on your personal website..." They will have the option whether or not to answer and elaborate more. Don't we build relationships based on shared interests with all kinds of people? Why should a T be an exception? I discussed with mine many times the info they present online and they always very much welcomed those conversations. Perhaps asked why I was interested, and then I said why. Sometimes I got responses that they did not want to talk about it and that was fine with me, clear and honest.

Perhaps your hesitation has something to do with fearing that the T would reject your intest?