I tested now on a second relatively new site with the new version 1.12.0. Same results. Notifications don’t work.
I skimmed through your notifications.php in modules/notifications. There seems to be a problem with the hook pp_send_notification_status_update. Only if I manually invoke send_notification_status_update() is this function ever called (instead of do_action(‘pp_send_notification_status_update’, $args);).
The problem then in send_notification_status_update() is that the recipients are note loaded which is probably caused by bugs in get_notification_recipients(). For instance, you use the $admins variable in this function that you never define. I suppose this variable is supposed to store the admin email address?
If I manually set email addresses for $recipients in your send_email() function, the notifications are sent properly.
I suggest you test on a fresh WordPress installation and load PublishPress from www.remarpro.com, so you are sure you test with the same release.