You could make a more distinct separation between notifications and projects and also remember that there is an awful lot of flexibility where notifications are concerned.
Look at what is more important to your users then take that as a starting point for how you design the notification part of your application. Is it more important when looking at general screens and lists that they know how many projects they have open at any point or that they are notified about events occurring on or to those projects?
You can also ask them more generally what information they need at any point to make their workflow more efficient and arrange your notifications accordingly. Observe them too, you might find that many users go through a cumbersome interaction pattern to find out info that you could easily display somewhere more convenient.
Once this question is answered you can decide what information you decide to display on the screen and whether any info is dropped. For example, on the list of project types the user might not actually need to know how many projects they have and prefer to see them marked clearly with 'needs attention' type notifications. A count might only be required on some other screen they seek out if they need that information.
A second thing you can do is grade notifications and use this to decide on how much a notification is pushed into the consciousness of a regular user. For the sake of example, you might have 'critical', 'needs attention' and 'general' notifications, where critical might be a deadline, 'needs attention' might be to verify a collaborators edit and general might be to read a comment.
You could then adjust the method of notification to be more prominent. 'Critical' might include an email, onload popup or clear definition in the master navigation bar, whereas 'general' might only appear when looking at the individual screen for a project.
So, to summarise:
Find out off your users what information they need at different stages of an interaction and use this to decide what information is displayed on the screens. Observe them in action to help with this.
Take the most important things and use methods that push into the users consciousness strongly to let them know.
Grade the importance of any notification.
Remember that a user can be notified in many ways. Email, text message, primary navigation space, on login, by marking with a count and by marking a part of a page that is changed are all ways that immediately spring to mind.