Welcome to the forum @Anna_Jos 
That might be tricky. Natively I don’t think there is functionality for that.
Assuming these updates are a kind of status-update, I’d use Status-updates instead of messages. This forces the person updating the status to at least add an indication of project health, and has other benefits. More info on status updates here: The 5 minute status update
The workaround I’d try is the following:
- Enable email notifications for status-updates (under: Settings > Notifications > Email notifications > Communication
- Create an email automation that: Checks if it is an update regarding this specific project, and if true forwards the email to the corresponding team.
This would require some tinkering and testing I’d guess. And as this is functionality outside of Asana and specific to your email client I don’t think this forum is the best place to continue discussing the specifics of this solution.
Note that this is a bit of a time-bomb, as this solution stops working as soon as you stop working there.
If you want some assistance with this feel free to reach out in DM to plan a free call.