Adding ThirdPartySetting to webform entity results in wrong module dependency
Please use hook_webform_third_party_settings_form_alter() in mymodule.module and discard the submit handler which should solve that:
use Drupal\Core\Form\FormStateInterface;

/**
 * Implements hook_webform_third_party_settings_form_alter().
 */
function mymodule_webform_third_party_settings_form_alter(&amp;$form, FormStateInterface $form_state) {

  /** @var \Drupal\webform\WebformInterface $webform */
  $webform = $form_state-&gt;getFormObject()-&gt;getEntity();

  // Do stuff.

  $form['third_party_settings']['email_element'] = [
    '#type' =&gt; 'select',
    '#options' =&gt; $options,
    '#title' =&gt; t('E-mail element'),
    '#default_value' =&gt; $webform-&gt;getThirdPartySetting('mymodule', 'email_element'),
  ];

  // Do not add submit handler.
}

Webform's WebformThirdPartySettingsManagerInterface wraps Core's ThirdPartySettingsInterface which is why I think you're seeing that behaviour.