Filter products on category AND tag

You can define taxonomy with post type.
Create and display separate categories and tags with taxonomy.
Example code:

add_action( 'init', 'artists' );
function artists() {
register_post_type( 'artists',
    array(
        'labels' => array(
            'name' => __( 'artists' ),
            'singular_name' => __( 'artist' )
        ),
        'public' => true,
        'has_archive' => true,
        'rewrite' => array( 'slug' => 'artists' ),
        'menu_icon' => 'dashicons-slides',
        'supports' => array('title','thumbnail','editor', 'comments'),
        // 'taxonomies' => array('category'),
        'exclude_from_search' => false,
    )
    
);

register_taxonomy(
      'artists_cat',
      'artists',
      array(
        'label'        => __( 'category' ),
        'public' => true,
        'rewrite'      => true,
        'hierarchical' => false,
        'capabilities' => array( 'edit_terms' => 'manage_categories' )
      )
    );

register_taxonomy_for_object_type( 'artists_cat', 'artists' );
}