Enable support for non-public Custom Post Type

By default, you can select only public post types in the Notification settings. To add a support for non-public post type you need to add it via a filter:

add_filter(
    'notification/settings/triggers/valid_post_types',
    function($postTypes)
    {
        // Slug is the key and Singular name is the value.
        $postTypes['non_public_post_type_slug'] = __('Non Public Post Type');
        return $postTypes;
    },
    10,
    2
);

Not all Merge Tags will be working properly for the private post type, ie. the permalink tag.