Notifying drupal user on publishing
Sounds like a perfect use case for the Menu Badges module, which can be used to add notifications to any menu item and/or menu tab of your choice. Here are some details about it (from its project page):

Provides a method for adding iOS-style badges to menu items. (see screenshot)


Because of how it integrates with the Views module, you basically reduce the solution specific to your question here to something like this:

Create an appropriate view about &quot;new pieces of content relevant to their page has been published&quot; (as in your question).
And create a menu item or menu tab for it.
Grant access to that view for those users who fit &quot;a fellow publisher within the Drupal permissions group&quot; (as in your question).
Perform the required Menu Badges configuration to tell it which menu item/tab you used for it in your view.

Refer to the video Defining Menu Badges with Views in Drupal (from the module maintainer) for more details. It shows a scenario that might be close to what you'd want to implement also.
PS: I'm assuming this question is about D7 ...