If you want to have cleaner URLs and want to delete the taxonomy part of the url

remove-taxonomie-slugs.php

// add to functions.php

// thanks to: https://rudrastyh.com/wordpress/remove-taxonomy-slug-from-urls.html

add_filter('request', 'rudr_change_term_request', 1, 1 );

function rudr_change_term_request($query){

    $tax_names = array('manufacturer', 'product_cat');
    // specify you taxonomy name here, it can be also 'category' or 'post_tag'

    // Request for child terms differs, we should make an additional check
    if( $query['attachment'] ) :
        $include_children = true;
        $name = $query['attachment'];
    else:
        $include_children = false;
        $name = $query['name'];
    endif;

    // if find product with name
    $posts = false;
    if (isset($query['attachment'])) {
        $posts = get_posts(array(
            'name' => $query['attachment'],
            'posts_per_page' => 1,
            'post_type' => 'product',
            'post_status' => 'publish'
        ));
    }
    if ( isset($posts) && !is_wp_error($posts) && isset($posts[0]) ) {
        $query['page'] = '';
        $query['product'] = $name;
        $query['post_type'] = 'product';
        $query['name']= $name;
        unset($query['attachment']);
        return $query;
    }

    foreach ($tax_names as $tax_name) {
        $term = get_term_by('slug', $name, $tax_name); // get the current term to make sure it exists
        if ( $term && !is_wp_error($term) ) { break; }// term found so don't search on}
    }

    if (isset($name) && $term && !is_wp_error($term)): // check it here

        if( $include_children ) {
            unset($query['attachment']);
            $parent = $term->parent;
            while( $parent ) {
                $parent_term = get_term( $parent, $tax_name);
                $name = $parent_term->slug . '/' . $name;
                $parent = $parent_term->parent;
            }
        } else {
            unset($query['name']);
        }

        switch( $tax_name ):
            case 'category':{
                $query['category_name'] = $name; // for categories
                break;
            }
            case 'post_tag':{
                $query['tag'] = $name; // for post tags
                break;
            }
            default:{
                $query[$tax_name] = $name; // for another taxonomies
                break;
            }
        endswitch;

    endif;

    return $query;
}


add_filter( 'term_link', 'rudr_term_permalink', 10, 3 );

function rudr_term_permalink( $url, $term, $taxonomy ){

    $taxonomies = array();
    $taxonomies[] = array('tax_name' => 'manufacturer', 'tax_slug' => 'manufacturer');
    $taxonomies[] = array('tax_name' => 'product_cat', 'tax_slug' => 'product_cat');
    // your taxonomy name here
    // the taxonomy slug can be different with the taxonomy name (like 'post_tag' and 'tag' )

    // exit the function if taxonomy slug is not in URL
    foreach( $taxonomies as $tax ) {
        if ( strpos($url, $tax['tax_slug']) === FALSE || $taxonomy != $tax['tax_name'] ) continue;

        $url = str_replace('/' . $tax['tax_slug'], '', $url);
    }

    return $url;
}