Thanks for your help!
I ran some more Tests. It seems that indeed also another agent is not notificated on new ticket assignment.
I checked the mail server logs and there is only connection if the mail address is used for the user, not if the agent is assigned.
I double checked the notification settings in admin panel. There is notification on new ticket disabled, notification on ticket assignment set to activated and assigned Team/agent.
Another idea why this did just stopped working, as it was working well until few days?