Is there a way to know when a specific search result is a best bet

To my knowledge there is not but can see it being a useful feature!

I was looking at this this morning. The module page mentions that it applies a class to results when using Search API Pages, and shows how to get the 'elevated' status form inside the set of results (i.e. for each item).

I needed a class on the view row, and handled it like this (in a .theme file):

use Drupal\views\ViewExecutable;

/**
 * Implements hook_views_pre_render()
 */
function mytheme_views_pre_render(ViewExecutable $view) {
  $view_id = $view->id();
  if ($view_id === 'sitewide_search' && $view->current_display === 'sitewide_search_page') {
    // hook_views_pre_render() appears to runs once per view (?); here we use
    // drupal_static to do our part only once.
    $processed = &drupal_static(__FUNCTION__, []);
    $cache_key = sprintf('%s:%s', $view_id, $view->current_display);

    if (isset($processed[$cache_key])) {
      return;
    }

    if ($view->query instanceof \Drupal\search_api\Plugin\views\query\SearchApiQuery) {
      $results = $view->query->getSearchApiResults();
      $result_items = $results->getResultItems();

      foreach ($view->result as $index => $row) {
        if (isset($result_items[$row->search_api_id])) {
          $row->bestbet_elevated = (bool) $result_items[$row->search_api_id]->getExtraData('elevated');
        }
      }
    }

    $processed[$cache_key] = TRUE;
  }
}

/**
 * Implements template_preprocess_views_view_list().
 */
function mytheme_preprocess_views_view_list(&$variables) {
  $view = $variables['view'];

  if ($variables['view']->id() === 'sitewide_search' && $variables['view']->current_display === 'sitewide_search_page') {
    foreach ($variables['rows'] as $index => &$row) {
      $result_row = $variables['view']->result[$index];

      if ($result_row->bestbet_elevated) {
        $row['attributes']->addClass('search-api-elevated');
      }
    }
  }
}

The mytheme_views_pre_render() implementation tags the row as elevated. After that, pretty much anything is possible. For our purposes, we only needed to render a class on that basis, but it should be possible to do other things like render the elevated item using a different view mode etc.

Sorry to disappear but I see we have the hook that does

    $item = $variables['item'];

    $variables['elevated'] = FALSE;
    if ($item->getExtraData('elevated')) {
      $variables['title_attributes']['class'][] = 'search-api-elevated';
      $variables['content_attributes']['class'][] = 'search-api-elevated';
      $variables['elevated'] = TRUE;

Is that what you were looking for @jwilson3?

Maybe we can do something for views

Took inspiration from #4 with small tweaks. Pushed to both 4.0.x and 3.0.x