The Assignee list is equivalent to the Teams Owner list in Teams.
So simply add new Teams Owners in this Teams / Channel, to build your assignee list in Ticketing App.
We made this choice so that you do not have to administrate a user list in addition to your Teams members and Teams owners list.
Note that if you just added a new Teams Owners, you might need to log out / log in again so that the Assignee list is being updated.
Have a great day!
Alex, TeamsWork Support