Add search to docs 404 page

[bmorelli25]

No matter how good our docs are, there will always be users hitting 404s. In addition to the redirect strategy being discussed in #1820, can we add search to our 404 page?

As an example, here's a documentation 404. Anyone who hits that page will see this:

It's fun, but it's not helpful. What would be helpful, is if the 404 page was able to display relevant search results based on the bad URL and provide a search box for users to craft their own searches. Based on the URL in this example, the 404 page might include something like this:

A quick google search shows that smart 404 pages like this are actually a feature of Swiftype: Building a smart 404 page with Swiftype. 🐶🥫