I love the idea of using advanced voice to do searching, however I think a small change will make it wasy better. I say small becuase you already have the feature so you only need to enable it a new way.
The first image shows how with standard voice ChatGPT displays images while in a chat, so if you could display search results while in an advanced voice chat that would be amazing. When the voice reads out all the response results (like resturants) people will get confused about what was said at the start, but if you show the results it will give them a rich audio and visual conversation.
First image shows normal voice with image, and second a mockup of my suggestion.
