Formalize patching of `book.js`

Inspired by #2571 and other similar changes I made myself, we need to come up with a proper system for maintaining our customizations to theme/book.js. That is, we need to store our modifications as patches or something very similar. Right now, our customizations are direct edits to the file.

The problem is that mdbook is somewhat coupled to it's theme: when we update mdbook to a new version, we run the risk of messing up the rendering if we don't update our (partial!) copy of the default theme.

I'm imagining a system where we:

1. Store the modifications as a set of patches.
2. Check that theme/book.js is truly equal to the original book.js file plus the applied patches in a GitHub action.
3. Some script which can update our mdbook version by updating the book.js file.

I'm probably missing some steps here! 😄

Cc @djmitche, @gribozavr.