REST API: Fix embedded items 'context' regression

[Mamaduka]

What

Fixes regression introduced in #43439, where navigation embed items were missing raw property values.

Why

The WP_REST_Server::match_request_to_handler mutates the $request object and sets the default context=view, which prevents setting context=embed as it's appropriate for these requests.

The unit tests missed regression since they didn't mimic the actual requests.

How

• Update the unit tests to match a request made by the client code.
• Set the context before matching a request to the handler.

Testing instructions

1. Checkout to the test update commit - 2a707e7.
2. Run the unit tests - npm run test:php -- --filter test_embedded_navigation_post_contains_required_fields.
3. They will fail.
4. Checkout to the fix commit - a11858d.
5. Rerun the unit tests; they should succeed now.
6. All other tests should be green.

Trac ticket: https://core.trac.wordpress.org/ticket/43439

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Props mamaduka, swissspidy, youknowriad, timothyblynjacobs.

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[youknowriad]

@TimothyBJacobs @spacedmonkey would you be able to help validate the fix here. This is a regression that happened during the 6.5 cycle, therefor, it would be good to land this fix on the same release.

[TimothyBJacobs]

This fix looks good to me as well.

I'd love if we could have unit tests that are covering this specifically as part of the WP_REST_Server tests, instead of the incidental coverage we are getting as part of the navigation controller. But I don't think that needs to block this from getting merged considering the timing.

[swissspidy]

Committed in https://core.trac.wordpress.org/changeset/57659