Hello! Thanks for outlining this workflow. As it turns out, there isn’t a currently available message template variable that would allow for the assignee information. https://help.front.com/en/articles/2306
BUT I’m still very happy you reached out about it. In fact, I encourage you to submit a request for it at this link.
This feature submission form is linked to our Product Ideas Portal which is accessible to all users. When features are submitted, they are listed in the Ideas Portal and can be upvoted by other Front customers who may want the same feature to improve their team's workflows. You'll receive an email update if your feature is developed and shipped! Exciting 
Most of the improvements you see to Front come from ideas and suggestions like yours, so thank you for making Front even better!