feat: support create on-demand search

[bxb100]

Since rust-lang/rust#144476 started using stringdex for on-demand search,

this extension's original search-index.js is not working anymore. So, I think maybe using on-demand search with the extension sandbox is a good idea, because the separte index script is small and can be cached by the browser, and naturally, the query is a single activity (it only supports @crate query), so the speed is not a problem.

Currently implementing only tests in Chrome.

Important

This code was generated by Codex; it is just an experimental test, not for merge.

[bxb100]

The docs.rs load search stringdex root-index depend on page data

https://github.com/rust-lang/rust/blob/794301af24b1ce06642419541b8f10d77aca939c/src/librustdoc/html/static/js/main.js#L415-L422

function getVar(name) {
    const el = document.querySelector("head > meta[name='rustdoc-vars']");
    const v = el ? el.getAttribute("data-" + name) : null;
    if (v !== null) {
        return v;
    }
    throw `rustdoc var "${name}" is missing`;
}

Current code does not deal with this compatibility problem, but I don't think assembling all index js files into a flat JSON to cache is a good idea