Account for FSE post types in rest endpoints.

[peterwilsoncc]

Is your enhancement related to a problem? Please describe.

RestApi\check_post_types_permissions() currently lists all post types available in the WordPress REST API. With the introduction of full site editing, this includes templates and other items that should probably never be shared.

Modify how the function searches for distributatble post types, possibly by changing to use Utils\distributable_post_types().

Designs

No response

Describe alternatives you've considered

TBA

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