The inbox with all notification mixed, and only limited filter capabilities, which doesn’t contemplate filtering per project, is still far from being good. If more filtering option is difficult to implement (and I think so, since, besides the many requests from users, there were no particular steps further) I would suggest creating a new project tab called “Project Inbox”, where all notification regarding this specific project, are collected. It would add context, and for project managers, which are more interested in following the project progress instead of doing tasks themselves, it would be a huge, huge improvement.
Thanks for sharing this feedback @Francesco_Canovi! I also think this could be a good idea, I’ve gone ahead and sent your feedback to our product team so they can considered in future updates.