How to fix translation in multi-language website + WooCommerce + AJAX checkout

I spent some time debugging and did some research, here is a small and quick fix that did the trick. I added this in my theme functions.php file, but it can be added in a plugin also.

add_filter( 'woocommerce_get_script_data', 'fix_ajax_handler_translation' );
if ( ! function_exists( 'fix_ajax_handler_translation' ) ) {
	/**
	 * Fix the lost translations on AJAX calls made in WordPress >= 5.0 with WooCommerce >= 3.5
	 * on checkout pages for example.
	 *
	 * @param array $params Script data.
	 * @return array
	 */
	function fix_ajax_handler_translation( $params ) {
		$locale = determine_locale();
		$lang   = ( ! empty( $locale ) ) ? strstr( $locale, '_', true ) : '';
		if ( empty( $lang ) ) {
			// Fail-fast, no need to check further. Fallback to the defaults.
			return $params;
		}
		if ( isset( $params['wc_ajax_url'] ) ) {
			$params['wc_ajax_url'] = $params['wc_ajax_url'] . '&lang=' . $lang;
		}
		return $params;
	}
}

Please note that if you use WordPress < 5.0 the native function determine_locale does not exist (it was introduced with 5.0), but you can use it as an alternative for get_user_locale.

I hope this helps anyone that encounters the same issue.