Auto merge of #92570 - jsha:rustdoc-search-refactor, r=GuillaumeGomez

Simplify rustdoc search test

Previously, rustdoc search attempted to parse search.js and extract out only certain methods and variables.

This change makes search.js and search-index.js loadable as [CommonJS modules](https://nodejs.org/api/modules.html#modules-commonjs-modules), so they can be loaded directly.

As part of that change, I had to separate execSearch from interacting with the DOM. This wound up being a nice cleanup that made more explicit what inputs it was taking.

I removed search.js' dependency on storage.js by moving hasOwnPropertyRustdoc directly into search.js, and replacing onEach with forEach in a path that is called by the tester.

r? `@GuillaumeGomez`

Demo: https://rustdoc.crud.net/jsha/rustdoc-search-refactor/std/?search=foo

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