Add icon to menu link that has system.admin as a parent
As per the answer by @mradcliffe, styles for the regular and active states would need to be created.  However you'd want to add them as a separate library which you'd include on admin pages, rather than edit core files.

So take the styles in @mradcliffe's answer, or whatever you determine to be correct, and save it to your module in css/webtrack-update-reminder-toolbar-icon.css.

In your module's webtrack_update_reminder.libraries.yml file, something like this:

toolbar-icon:
  version: 1.0
  css:
    theme:
      css/webtrack-update-reminder-toolbar-icon.css: {}


Then in your module's webtrack_update_reminder.module file, something like so:

/**
 * Implements hook_page_attachments().
 */
function webtrack_update_reminder_page_attachments(array &amp;$attachments) {
  $is_admin = \Drupal::service('router.admin_context')-&gt;isAdminRoute();
  if ($is_admin){
    $attachments['#attached']['library'][] = 'webtrack_update_reminder/toolbar-icon';
  }
}


That should be all that's needed to load the library (i.e. your stylesheet) on any admin pages, which will in turn apply your styles to the toolbar item and show your custom toolbar icon.