Dynamically generate Form API select list of routes to page displays of a known View

Given a known View, how would one dynamically generate a Form API select list of the routes to its Page Displays?

In my case, I have a Search API View (view.search) with a default site-wide search page (view.search.page_1) and separate search pages for different site sections, or "micro-sites" (e.g., view.search.page_2, view.search.page_3, etc.)

I have coded a custom block to replace the Drupal core Search form, which redirects to the site-wide search page, passing the fulltext query parameters as $link_options:

  /**
   * {@inheritdoc}
   */
  public function submitForm(array &$form, FormStateInterface $form_state) {

    // Redirect to a search page, appending search keys.
    $search_route = 'view.search.page_1';
    $search_url = Url::fromRoute($search_route);
    $link_options = [
      'query' => [
        'search_api_fulltext' => $form_state->getValue('keys')
      ],
    ];
    $search_url->setOptions($link_options);

    $form_state->setRedirectUrl($search_url);
  }

Next, I would like to provide per-block configuration in the Block Plugin class implementation, so that the redirect route can be selected by a site admin when placing an instance of the block.

I'm about to hard-code this form select element, but it would be nice if the list would automatically update later if a new display were to be added to the View.

In a drush php:cli, I can use the entity type manager to load the View storage:

>>> $view = \Drupal::entityTypeManager()
  ->getStorage('view')
  ->load('search')
  ->getExecutable();

And I can call a specific display as long as I know its machine name:

>>> $display = $view->getDisplay('page_2');

But there does not seem to be a $view->getDisplays() method:

>>> $displays = $view->getDisplays();
PHP Error:  Call to undefined method Drupal\views\ViewExecutable::getDisplays() in Psy Shell code on line 1

In my module, I don't need to actually deal with any of the usual Views API stuff (e.g., filter and sort criteria, rendering a display, etc.). I just need the machine names of valid page displays so I can concatenate them with 'view.search.' . $displayname and pass that to Url::fromRoute() so my new Form knows where to redirect its query.