If you just want to find out about new posts being made, I think I would follow the RSS feed of either recent posts or recent topics. That way you could see when new things are being posted. You could set up and RSS to Email thing and have an email sent when there are new items in the RSS feed if you don’t care for RSS.
If you want to moderate new posts and new topics, before they’re visible, you might want the BB Moderation Hold plugin:
https://bbpress.org/plugins/topic/bb-moderation-hold/
That was good for older version of bbPress. Not sure if it still works.
