Integrate CI emails into notification system
This is somehow a follow up from #3976 (closed), which described what we want to see from the emails. A corresponding merge request !6019 (merged) is under development for adding the new emails into a new pipeline service. However to make the best experience, we are better off having this integrated into the notification system, rather than a service which people needs to setup for each projects.
#3976 (closed) is already quite long so I would like to have this issue serving as a new thread for having this integrated as part of the notification system. I'll begin investigating how to do this properly.