Save Contact Form 7 Submissions in the Admin

add_action( 'init', function () {
    register_post_type( 'wpide_cf7_message', array(
        'labels'          => array( 'name' => 'Form Messages', 'singular_name' => 'Form Message', 'menu_name' => 'Form Messages' ),
        'public'          => false,
        'show_ui'         => true,
        'show_in_menu'    => true,
        'menu_icon'       => 'dashicons-email-alt',
        'supports'        => array( 'title', 'editor' ),
        'capability_type' => 'post',
        'capabilities'    => array( 'create_posts' => 'do_not_allow' ),
        'map_meta_cap'    => true,
    ) );
} );

add_action( 'wpcf7_mail_sent', function ( $contact_form ) {
    $submission = class_exists( 'WPCF7_Submission' ) ? WPCF7_Submission::get_instance() : null;

    if ( ! $submission ) {
        return;
    }

    $lines = array();
    foreach ( (array) $submission->get_posted_data() as $key => $value ) {
        if ( 0 === strpos( $key, '_' ) ) {
            continue;
        }
        $lines[] = '<strong>' . esc_html( $key ) . ':</strong> ' . nl2br( esc_html( is_array( $value ) ? implode( ', ', $value ) : (string) $value ) );
    }
    $lines[] = '<strong>Page:</strong> ' . esc_url( (string) $submission->get_meta( 'url' ) );

    wp_insert_post( array(
        'post_type'    => 'wpide_cf7_message',
        'post_status'  => 'private',
        'post_title'   => sprintf( '%s – %s', $contact_form->title(), wp_date( 'Y-m-d H:i' ) ),
        'post_content' => wp_kses_post( implode( "<br>\n", $lines ) ),
        'meta_input'   => array( '_wpide_cf7_form_id' => (int) $contact_form->id() ),
    ) );
} );