rustdoc: dedup search form HTML

This change constructs the search form HTML using JavaScript, instead of plain HTML. It uses a custom element because

- the [parser]'s insert algorithm runs the connected callback synchronously, so we won't get layout jank
- it requires very little HTML, so it's a real win in size

[parser]: https://html.spec.whatwg.org/multipage/parsing.html#create-an-element-for-the-token

This shrinks the standard library by about 60MiB, by my test.