REST API: Ensure rest_controller instantiates the post type's declared REST controller class.

Ensures that the ::get_rest_controller() method will always return an instanceof the expected controller class, or null.
Removes unused private static property $post_type_controllers.

Props dlh, TimothyBlynJacobs.
Fixes #45677.


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git-svn-id: https://core.svn.wordpress.org/trunk@46233 1a063a9b-81f0-0310-95a4-ce76da25c4cd