Provide support for the default WP post lookup admin feature

[brandwaffle]

Is your enhancement related to a problem? Please describe.

This feature would speed up the ajax-based post lookup that happens when you click on the Link button in Gutenberg and search for a post on the site.

Describe the solution you'd like

Take over the search behavior at /wp-json/wp/v2/search?search=&per_page=20&type=post&_locale=user if the plugin has the Protected Content feature activated. Optional: consider activating this if Search is active, limited obviously to published content. Might not be totally intuitive, but then again if this is for linking it would usually make sense to only show live articles (i.e. those that have a URL).

Designs

None.

Describe alternatives you've considered

Open to discussion :)

Additional context