Improve relevance for doc search results

[anton-trunov]

For instance, if I'm interested in searching for "as remaining" in the docs, the most relevant results which include the full string are not at the top of the search results box.

[novusnota]

This was achieved by moving to the Starlight documentation framework with the Pagefind search engine that comes with it.

[anton-trunov]

No, it's not fixed:

[novusnota]

Note to self to use https://pagefind.app/docs/ranking/ available in the latest Starlight release 0.31.0. This upgrade introduces breaking changes, so it should not be done by the dependabot.