Investigate new internal search engine, like Algolia

## Why are we implementing it? (sales eng)

We would like more control over weighting docs pages for certain search terms. The current search engine is provided by Read The Docs and operates as a sort of black box.

See how difficult it would be to override the Sphinx behavior. This issue makes it seem tricky: https://github.com/sphinx-doc/sphinx/issues/3812

### What are the typical use cases?

This is for people using the internal docs search box in the upper left.