Sounds like it is only anonymous if you fully trust the app. That app has all your information, and the site you are trying to access. And I bet it is completely closed source. It also likely has logs about what sires it is giving information to. Not who’s info in that log. But elsewhere it probably has logs on who’s id it verified. Get access to both, and software can start to crunch the numbers and figure out who went where. That if course is assuming they don’t decide in the future that it is worth just keeping that data together in one spot. There is just no entity that could manage that app which wouldn’t have a motive to use the data and power it has.