I'm pretty sure I predicted how OpenAI was going to use a browser if they had one exactly how they are doing it now. (Back then it was related to them buying Chrome if Google had gotten forced to do sell it)
Not really, I just chose the most simple implementation which is only a bunch of <details><summary>...</summary>...</details> tags. The behavior you describe would require some JavaScript on top. I'm not against that, I just didn't get to it yet.
edit: I just learned you actually don't need JS, just a "name" attribute. That's super nice