I'm working though my second playthrough on a higher difficulty, and I'm really appreciating how many different stories and options that show up based on your choices, and how much I missed or didn't fully realize the first time around. I just haven't gotten tired of playing out the story of Woedica's and Thaos' 2000 year long con.
In fact, yesterday I was completely blown away by the clever storytelling in the main quest. I sort of realized that Lady Webb was able to extract information from Thaos, but this time I really appreciated the cleverness of Lady Webb. Knowing that you were a watcher, and presumably figuring that Thaos would be clever enough to try to derail the animancy hearings, which would surely lead to her encountering him, she was able to extract the information from Thaos. Thaos, for all his planning, does not know that Lady Webb has been speaking to the watcher, so could not know that she would still be able to tell the details about where to go regarding his plans. Knowing that Thaos was going to kill her, she still extracted the information because she knew you'd be able to read her, or at least that was her gamble. I also realized that at the very end, though you are unable to extract this information, Thaos allowed her to see the truth of his plan and about the nature of the gods, or at least that is what I gather from her reaction. Why? Because she was his lover, and when you're bearing a secret, it is only human nature to have a desire to tell that to someone, even if you intend to immediately silence them.
My question is as follows: When does Thaos become aware, or at least strongly suspect, that you are a watcher? I am aware that fairly early on he realizes you are tailing him because of the assassins and the fact that he tells you as much during the encounter in First Fires. I gather, from what I mentioned above, that he is not aware of your nature until some point later on because otherwise he would never have allowed, or at least taken steps to avoid, the reading of the soul of Lady Webb by the watcher.