It's not something you can query, but many extensions inject JS or markup into the DOM, and you could scan the DOM for such changes. For instance, password managers inject a "fill password" button into login fields that you could detect.
While I agree that PW managers alter the DOM elements that could be identified, I've never seen 1Pass inject a button like this. I have however seen it add data attributes to elements though. What PW Managers add a button like that?