How do I pass a response from a Webform custom handler back to Drupal to display on the confirmation page
Your two options are… 

OPTION 1: Add the SOAP API's response value  as a hidden element's value using something like 

$webform_submission-&gt;setElementData('response_value', $response-&gt;value);
$webform_submission-&gt;resave();


OPTION 1: Store the response in $_SESSION and use 

\Drupal\webform\Plugin\WebformHandlerInterface::confirmForm
\Drupal\webform\Plugin\WebformHandlerInterface::preprocessConfirmation


to alter the confirmation message or page.