Adds new hooks (rest_save_sidebar, rest_delete_widget, rest_after_save_widget)
to the widgets REST API and uses them to delete the fresh_site option when
updating widgets via the REST API. This ensures that starter content isn't
loaded in the Customizer after a user makes changes.
Fixes#53317.
Props kevin940726, garrett-eclipse, andraganescu, hellofromtonya.
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