Drupal - How to expose the user's email on the user's detail page?

By default the mail field is not configurable in view modes.

You can change this in a custom module. Place this hook in mymodule.module

function mymodule_entity_base_field_info_alter(&$fields, $entity_type) {
  if ($entity_type->id() == 'user') {
    if (isset($fields['mail'])) {
      $fields['mail']->setDisplayConfigurable('view', TRUE);
    }
  }
}

and you'll find the mail field in the Manage Display page.