wp-allow-private-post-parent-links.php

<?php

function preseto_rest_with_extra_post_stati( $query, $request ) {
        if ( current_user_can( 'read' ) ) {
                $query['post_status'] = [ 'publish', 'private' ];
        }

        return $query;
}

add_filter( 'rest_post_search_query', 'preseto_rest_with_extra_post_stati', 10, 2 );
add_filter( 'rest_post_query', 'preseto_rest_with_extra_post_stati', 10, 2 );
add_filter( 'rest_page_query', 'preseto_rest_with_extra_post_stati', 10, 2 );