Customize: Use client-side templates for rendering base controls

[westonruter]

This is a follow-up on #30738. See patches on that ticket. Eliminating server-side rendering of the control content for server-side registered controls was not included as part of 4.9 due to it being a big change and it got too late in the release.

This will necessarily need to include support for dropdown-pages which we didn't implement in #30738, since we ran out of time and wanted to rely on REST API for fetching the pages.

See implementation of dropdown-pages control template here: ​https://gist.github.com/westonruter/00c351830e0a15cef7672b748720a7ff

We should go ahead and implement the dropdown-pages control using the approach in that ​gist and not wait for REST API integration because the approach using wp_dropdown_pages() will be better for back-compat. And at the very least, by using this template we'll cut down on at least half of the wp_dropdown_pages() calls for a given page load, because the template will then be re-used for both the controls for the homepage and posts page.