On save_post need to wp_insert_post and save partent post id to child post and child post id to parent post

Here’s an updated version of your code:

add_action('save_post', array($this, 'save_post_type_example_meta_boxes'));
function save_post_type_example_meta_boxes($post_id)
..........

    if (...) {
        $new_custom_post = array(
            'post_title'    => $title,
            'post_content'  => '',
            'post_status'   => 'publish',
            'post_author'   => 1,
            'post_type'   => 'custom_post_type',
            'meta_input'   => array(
                'meta_1' => 'X',
                'parent_post_id' => $post_id,
            ),
        );

        // Prevent this action from running twice.
        remove_action( 'save_post', [ $this, 'save_post_type_example_meta_boxes' ] );
        $child_post_id = wp_insert_post( $new_custom_post );
        // Readd the action.
        add_action('save_post', array($this, 'save_post_type_example_meta_boxes'));
    }

    update_post_meta($post_id, 'child_post_id', $child_post_id);
    ......
    if(isset($_POST['meta_x_post'])) {
        $meta_x = sanitize_text_field($_POST['meta_x_post']);
        update_post_meta($post_id, 'meta_x', $meta_x);
    }
...
}

And here’s what I changed:

• The incoming post ID to save_post_type_example_meta_boxes should be what you want to use as your “parent” post ID.
• You should temporarily remove your hook to save_post so that it doesn’t try to run on that action over and over again.
• As noted by @Milo, wp_insert_post returns a post ID on success, so that would give you the “child” post ID.