Investigate more advanced search

**Is your feature request related to a problem? Please describe.**

Sometimes the search doesn't display the most relevant results or misses relevant sections in the service. It seems to rely mainly on exact matches, which then requires prior knowledge of what you're searching for.

**Describe the solution you'd like**

Would like for the search to be more based around natural language so it's easier for people to look for things on the site without knowing what exists first.

Most obvious thing to try above the standard search.json indexing provided by Quarto natively, would be to integrate with the [Algolia API](https://www.algolia.com/products/search-and-discovery/hosted-search-api/) as it's already suggested in the [Quarto documentation](https://quarto.org/docs/websites/website-search.html#overview) and has clear steps for implementation.

**Describe alternatives you've considered**

Honestly, nothing else really yet. Algolia's API seems like the easiest first option to try out given it's already suggested in the documentation.

**Additional context**

Some example searches that seem sub-par so far: