Update custom field values on edit address page woocommerce

Question

I know it’s too late to answer your question but its too easy and simple:
Your code is always exiting from function at line 6 because the results of your if expression always returns true at line 5:

if ( isset( $wp_query->query_vars['edit-address'] ) && $wp_query->query_vars['edit-address'] != 'billing' ) {
// above expression results would be: (either false or true) != (string) => this always return true
            return $address;
}