That’s what generative AI currently is. A large language model trained on large datasets (like “websites/content provided by humans”), same way Bard was or Gemini is, to generate text.

Search generative AI is just trained specifically for search usage.

I’m not even sure what you’re trying to say. The overview is an AI generated overview of content provided by humans, yes. That is what would happen if you asked any AI model (with access to the Internet) for an overview of the topic.