I'm beginning to understand that there are many definitions of "search engine", and that has caused much confusion to me. I would say that the use case you describe here is nothing even close to the sort of problem that a search engine addresses. It's more of a knowledge engine thing (and even that's a poor fit, really).
When I think "search engine", I think of something that searches for web pages. What I want as a result isn't an answer, meal plan, grocery list, or any of that higher-order stuff. I want a list of websites.
This reinforces my fear that this sort of approach might kill actual search engines. That would be a pretty serious loss to me, and a further reduction in the usefulness of the web. But saying that is not disparaging things like ChatGPT at all. They address a different, and valid, need.
I just hope we don't lose an important tool in the process.