Add customer note when the order meta is updated

Is it possible to add note to customer after change order meta. I use this code and it works with add_order_note(), but not with set_customer_note().

add_action( 'woocommerce_process_shop_order_meta', 'save_extra_details', 10, 3 );    
function save_extra_details( $post_id, $post ) {
	
	$meta_delivery_date = get_post_meta( $post_id, '_delivery_date', true );
	
	if ( $_POST[ '_delivery_date' ] != $meta_delivery_date ) {
		$order = wc_get_order( $post_id );
		$note = 'Delivery date was changed from ' . date("m/d/Y", strtotime($meta_delivery_date)) . ' to ' . date("m/d/Y", strtotime($_POST[ '_delivery_date' ]));
		//$order->add_order_note( $note );
		$order->set_customer_note($note);
		$order->save();
);
    }
    
    update_post_meta( $post_id, '_delivery_date', wc_clean( $_POST[ '_delivery_date' ] ) );
    
}

Is there any way to inform customer about order meta changes? Thanks