Backport: Introduce new dedicated media search handler and add new label field search handler

[petitphp]

This trac ticket is for backporting PHP changes for ​https://github.com/WordPress/gutenberg/pull/58638.
This change add a new REST search media handler and add a new label field to allow translating postType.

See: ​https://github.com/WordPress/gutenberg/issues/21377

This change is related to a ​PR in gutenberg to display localize name for suggestions in the link component.

This change felt too complex to be added to the gutenberg repository and backported afterward. Also I wanted to be able to update existing tests for the REST search handler.

This PR contain two changes :

• Add a new label property in the WP_REST_Search_Controller and update existing handlers to fill this property accordingly
• Add a new WP_REST_Media_Search_Handler handler to uniformize the shape of the data send back by the search endpoint between all types.

It looks like the associated Gutenberg PR hasn't been merged yet. I'm leaving feedback there for now.