As of right now (July 24), we do not send out any notifications to other users when a new Project Update is posted.
With that said, we are currently working on building a new Notifications system that will create in-app notifications and send out an email for important Project activities. This new notification system should be available by September 2024.
In the meantime, whenever you post a Project Update the activity will be posted to the Project Activity Log and your overall Workspace Activity Log, so the Activity Logs will be a good place to visit to get visibility into what's happening on all of your projects.