Sanitize custom checkout fields data in WooCommerce

Solution:

If you look to the related Official Documentation linked in your question, you’ve got this snippet:

/**
 * Update the order meta with field value
 */
add_action( 'woocommerce_checkout_update_order_meta', 'my_custom_checkout_field_update_order_meta' );

function my_custom_checkout_field_update_order_meta( $order_id ) {
    if ( ! empty( $_POST['my_field_name'] ) ) {
        update_post_meta( $order_id, 'My Field', sanitize_text_field( $_POST['my_field_name'] ) );
    }
}

In your case you don’t need that as address fields are already processed by Woocommerce.

For custom special fields: The answer is yes (which is not your case)

As you can see in this code they use sanitize_text_field() WordPress function, when saving the submitted data to database with update_post_meta() function…

This is only for custom checkout fields and not for existing checkout fields, that already get their own process…