For what it's worth, I think LLMs are very compatible with the style of interview you describe here. For people for whom LLMs have become a part of their workflow, seeing how they interact with them is just one more way to get a sense for how they work and think about things. If it doesn't come up, that's find too! But I don't see any reason not to accept their usage in your interviews.
(But I do think it's key to ask them to screenshare if they're going to go that route, so that you can actually see their interaction to get that signal.)