Currently, email notification is only sent to a group when a
new ticket is submitted
It is not appropriate for someone in, say, the Linux Admin group, to assign an existing ticket to a technician in, say, the Windows Admin group since that Linux admin does not necessarily know who in the Windows Admin group is most appropriate to process the ticket.
Hence there is a need to be able to automatically send an email to a group when an
existing ticket is assigned to a group.
Suggest that you amend the following notification on the Technician's Notifications configuration page:
"Alert group members by email when a new request is added to the group" to read
"...any request..." and change the code accordingly.
You could also amend the Tecnician Notification on the Technician Groups page in the same way.
I would suggest that the former would be the more appropriate way to implement this feature.