I am trying to change the default structure of the woocommerce product url to include the author username.
The default url for woocommerce products in my installation is as so:

https://<site_url>/product/<product-name>

I want to change it to something like this:

https://<site_url>/product/<author-username>/<product-name>

This is the code that I have so far:

function so_pre_get_posts( $query ) {
    // check if the user is requesting an admin page
    // or current query is not the main query
    if ( is_admin() || ! $query->is_main_query() ){
        return;
    }
  //since the author is not included in woocommerce query vars add author username to query_vars
  $post_type = get_query_var( 'post_type' );
  if($post_type === 'product'){
    $post_name = get_query_var( 'name');
    if ( $post = get_page_by_path($post_name,OBJECT,'product') ){
      $id = $post->ID;
      $author_id = get_post_field( 'post_author', $id );
      $author = get_userdata($author_id);
      $author_username = $author->user_login;
      $query->set( 'seller',$author_username);
    }else{
      return;
    }
  }
}

//add rewrite rules
function so_rewrite_tag_rule() {
  add_rewrite_tag( '%seller%', '([^&]+)' );
    add_rewrite_rule('^product/([^/]+)/([^/]+)/?$', 'index.php?seller=$matches[1]&name=$matches[2]','top');
  flush_rewrite_rules();
}
add_action( 'pre_get_posts', 'so_pre_get_posts', 1 );
add_action('init', 'so_rewrite_tag_rule', 10, 0);

However when I visit the product page for any product it still resolves to the default woocommerce
permalink structure. I made sure to flush the permalinks in my code so I have no idea what the issue is.