REST API: Test schema registration for required fields.

[rmccue]

Follow-up from #38792.

For all endpoints included in WordPress core, we want to make sure arguments and parameters are consistently registered and expose a nice, stable API to the world. While we can check this manually, building it into the unit tests is even better.

@jnylen0 wrote an initial version ​in Node-based JS, so we can port this to PHP and use the built-in schema rather than sending a HTTP request.