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.

tests/rustdoc-gui/sidebar-source-code-display.goml

@@ -4,7 +4,7 @@ javascript: false
 go-to: "file://" + |DOC_PATH| + "/src/test_docs/lib.rs.html"
 // Since the javascript is disabled, there shouldn't be a toggle.
 wait-for-css: (".sidebar", {"display": "none"})
-assert-css: ("#sidebar-button", {"display": "none"})
+assert-false: "#sidebar-button"
 
 // Let's retry with javascript enabled.
 javascript: true