Woocommerce: Extra added country field not taking value from database

Unless I’m missing something, you’re collecting the data through the post, validating it, and storing it, but I’m not seeing how you intended to display the billing_country in the checkout template.

Since the billing_country data is stored in the user meta, you could display it in your checkout template using get_user_meta:

<?php

  $billingCountry = get_user_meta($customer_id, 'billing_country', true);

  echo $billingCountry;

?>