Review

First thing I noticed is that you copied the entire add to cart form, I would recommend you extend the addToCart form instead of reimplementing the entire form. In order to make ajax work for we changed the actions function like so:

/**
   * {@inheritdoc}
   */
  protected function actions(array $form, FormStateInterface $form_state) {
    $actions['submit'] = [
      '#type' => 'submit',
      '#value' => $this->t('Add to cart'),
      '#submit' => ['::submitForm'],
      '#ajax' => [
        'callback' => '::ajaxSubmit',
        'wrapper' => $this->getAddToCartWrapperId(),
      ],
    ];

    return $actions;
  }

And added the ajaxSubmit function:

public function ajaxSubmit(array &$form, FormStateInterface $form_state) {
    $response = new AjaxResponse();
    $messagesRender = StatusMessages::renderMessages(NULL);
    $messages = \Drupal::service('renderer')->renderPlain($messagesRender);
    // Remove any existing messages
    $response->addCommand(new RemoveCommand('.messages'));
    if ($form_state->hasAnyErrors()) {
      $response->addCommand(
        new PrependCommand('.main-content', $messages)
      );
      return $response;
    }
    else {
      $form_state->setRebuild(FALSE);
    }
    return $form;
  }

Not sure if you need to return the status messages in case of errors but for our implementation we needed it. But after this is worked.

I can make a small patch if you would like it but I am not sure when it will be. Let me know what you think and how it works out.

// Jesper