I would add a feature called "announcements" which would allow a project make infrequent announcements that would show up on the timeline of all the project's "starrers".
Have "I'm subscribing to this project's announcements" be a different item than starring. But when they turn the feature on, make this checked for everyone's starred repos. And when a user stars a new repo, have that automatically subscribe the user to the project's announcements.
The reasoning? If you star a project, you're usually interested in the project's announcements, but not always. In particular, some projects might have high-volume announcements. That's perfectly okay, if the particular project culture wants them; but users who view high-volume announcements as annoyances or even borderline spam can still turn that particular project's announcements off, and still be able to have it starred.