Woocommerce product rewrite rules not working

No need to add additional rewrite rule for that, WooCommerce already provide a way to mess with product permalink. Visit Wp Admin > General > Permalink page, and use /product/%author%/ as Product permalinks value. This will organize the product url as you need.

However, WooCommerce won’t replace %author% tag with product’s author as like we see with post permalink, so you have to replace the tag using post_type_link filter.

// replace %author%

add_filter( 'post_type_link', 'wpse_post_type_link', 20, 2 );

function wpse_post_type_link( $permalink, $post ) {
    if ( 'product' === $post->post_type && false !== strpos( $permalink, '%author%' ) ) {
        $author = get_the_author_meta( 'user_nicename', $post->post_author );
        $permalink = str_replace( '%author%', $author, $permalink );
    }

    return $permalink;
}