adding filtering by attributes to products

Hello
thanks for the support and great plugin!
Please tell me – I have a code and it works fine for filtering in the Product by the pa_brand attribute. (code below)

add_action( 'restrict_manage_posts', 'aws_brand_products_sorting' );
function aws_brand_products_sorting() {
global $typenow;
$post_type = 'product'; // change to your post type
$taxonomy = 'pa_brand'; // change to your taxonomy
if ($typenow == $post_type) {
$selected = isset($_GET[$taxonomy]) ? $_GET[$taxonomy] : '';
$info_taxonomy = get_taxonomy($taxonomy);
//$selected = isset($_GET[$info_taxonomy->name]) ? $_GET[$info_taxonomy->name] : '';
wp_dropdown_categories(array(
'show_option_all' => __("Brand {$info_taxonomy->label}", "aws-multi-functions"),
'taxonomy' => $taxonomy,
'name' => $taxonomy,
'orderby' => 'name',
'selected' => $selected,
'show_count' => true,
'hide_empty' => true,
));
};
}
add_filter( 'parse_query', 'aws_brand_products_sorting_query' );
function aws_brand_products_sorting_query( $query ) {
global $pagenow;
$post_type = 'product'; // change to your post type
$taxonomy = 'pa_brand'; // change to your taxonomy
$q_vars = &$query->query_vars;
if ( $pagenow == 'edit.php' && isset($q_vars['post_type']) && $q_vars['post_type'] == $post_type && isset($q_vars[$taxonomy]) && is_numeric($q_vars[$taxonomy]) && $q_vars[$taxonomy] != 0 ) {
$term = get_term_by('id', $q_vars[$taxonomy], $taxonomy);
$q_vars[$taxonomy] = $term->slug;
}
}

But I need to add more filtering on the pa_seller attribute.
I am changing the name of the attribute – please see the code below. – but it doesn’t work.

add_action( 'restrict_manage_posts', 'aws_seller_products_sorting' );
function aws_seller_products_sorting() {
    global $typenow;
    $post_type = 'product'; // change to your post type
    $taxonomy  = 'pa_seller'; // change to your taxonomy
    if ($typenow == $post_type) {
        $selected      = isset($_GET[$taxonomy]) ? $_GET[$taxonomy] : '';
        $info_taxonomy = get_taxonomy($taxonomy);
        //$selected      = isset($_GET[$info_taxonomy->name]) ? $_GET[$info_taxonomy->name] : '';
        wp_dropdown_categories(array(
            'show_option_all' => __("Seller {$info_taxonomy->label}", "aws-multi-functions"),
            'taxonomy'        => $taxonomy,
            'name'            => $taxonomy,
            'orderby'         => 'name',
            'selected'        => $selected,
            'show_count'      => true,
            'hide_empty'      => true,
        ));
    };
}
add_filter( 'parse_query', 'aws_seller_products_sorting_query' );
function aws_seller_products_sorting_query( $query ) {
    global $pagenow;
    $post_type = 'product'; // change to your post type
    $taxonomy  = 'pa_seller'; // change to your taxonomy
    $q_vars    = &$query->query_vars;
    if ( $pagenow == 'edit.php' && isset($q_vars['post_type']) && $q_vars['post_type'] == $post_type && isset($q_vars[$taxonomy]) && is_numeric($q_vars[$taxonomy]) && $q_vars[$taxonomy] != 0 ) {
        $term = get_term_by('id', $q_vars[$taxonomy], $taxonomy);
        $q_vars[$taxonomy] = $term->slug;
    }
}

Please help, what am I doing wrong with the second code and pa_seller attributes?
Why is the second code not filtering? (the filtering and selection box appears, but the filtering itself does not occur).

Thanks a lot for your help