Importing Custom Taxonomy Through CSV into WooCommerce

I have created two custom taxonomies using the CPT UI plugin named Designers (rug_designers) & Product Lines (product_line). I am working on importing products via a CSV into WooCommerce using the built-in WooCommerce importer tool (not the Product CSV Import Suite). I was able to follow this guide to register the Custom Columns in the import with automatic mapping, however, whenever I upload the CSV file the data does not save to the custom taxonomy.

Here is the current code I have in my functions.php file

 * Register the 'Custom Column' column in the importer.
 *
 * @param array $options
 * @return array $options
 */
function add_column_to_importer( $options ) {

    // column slug => column name
    $options['rug_designers'] = 'Designers';
    $options['product_line'] = 'Product Line';

    return $options;
}
add_filter( 'woocommerce_csv_product_import_mapping_options', 'add_column_to_importer' );

/**
 * Add automatic mapping support for 'Custom Column'. 
 * This will automatically select the correct mapping for columns named 'Custom Column' or 'custom column'.
 *
 * @param array $columns
 * @return array $columns
 */
function add_column_to_mapping_screen( $columns ) {
    
    // potential column name => column slug
    $columns['Designers'] = 'rug_designers';
    $columns['designers'] = 'rug_designers';
    $columns['Product Lines'] = 'product_line';

    return $columns;
}
add_filter( 'woocommerce_csv_product_import_mapping_default_columns', 'add_column_to_mapping_screen' );

/**
 * Process the data read from the CSV file.
 * This just saves the value in meta data, but you can do anything you want here with the data.
 *
 * @param WC_Product $object - Product being imported or updated.
 * @param array $data - CSV data read for the product.
 * @return WC_Product $object
 */
function process_import( $object, $data ) {
    
// This appears to be part I am having trouble with, I have even tried it with just the 'rug_designers'

    if ( ! empty( $data['rug_designers'] ) || ! empty( $data['product_line'] ) ) {
        $object->update_meta_data( 'rug_designers', $data['rug_designers'] );
        $object->update_meta_data( 'product_line', $data['product_line'] );
    }

    return $object;
}

As my comment above mentions, I believe the issue to be in the process import function. I have tried to run this without the ‘product_line’ code and was still unable to get the ‘rug_designers’ to update the data upon csv import.

I would highly appreciate any suggestions. Thanks.