Bounced emails are often a pain point for Marketing/Sales, but in Support it can be the difference between losing a client or not. Despite this, there is no easy way for tickets to have any sort of action if a support email bounces. Automations are allowed for Contacts, etc, but nothing remotely close for tickets.
I believe the easiest solution would just be to allow activity actions such as bounce to work for tickets the same way they do for Contacts, but there may be other solutions that work as well. Either way this is a critical need for support teams.