Fix searchbox for package docs

[oraNod]

Follows up on #3309

@felixfontein mentioned that the searchbox from the package docs does not behave the same way as core docs: #3309 (comment)

Looking at Receptor and ansible-core docs on RTD:

• https://docs.ansible.com/projects/receptor/en/latest/
• https://docs.ansible.com/projects/ansible-core/devel/

Both of these projects use the sphinx-ansible-theme as the package docs. If you enter the searchbox in the left nav, you can see that Read the Docs search takes over.

Looking at the package docs at: https://docs.ansible.com/projects/ansible/latest/index.html

If you enter the searchbox in the left nav, it does not use Read the Docs search.

Edit: Removing some details that turned out to not be very relevant.

[oraNod]

Taking more of a look I think we need to add an event listener to trigger Read the Docs search. There's a custom event that opens the RTD server-side search form when you focus on the searchbar.

Because the package docs are built on GitHub runners outside the RTD build environment, that custom event isn't added.

We could add our own listener and include it in the Sphinx build for the package docs.

document.addEventListener("DOMContentLoaded", function() {
    const searchInput = document.querySelector(".st-default-search-input");
    
    if (searchInput) {
        searchInput.addEventListener("focusin", () => {
            const event = new CustomEvent("readthedocs-search-show");
            document.dispatchEvent(event);
        });
        
        //Should we also trigger on click?
        searchInput.addEventListener("click", () => {
            const event = new CustomEvent("readthedocs-search-show");
            document.dispatchEvent(event);
        });
    }
});

And then update conf.py with something like this, but needs to be conditional on the ansible tag:

html_js_files = [
    ("readthedocs-search.js", {"defer": "defer"}),
]

I've tried this in my fork and deployed to https://oranod-package-doc-builds.readthedocs.io/

@felixfontein FYI ^