This is occurring because the Type Categories are either not created or not set to "Active." To verify this go to When you go to Admin > Applications > [ticketing app] > Shared Ticketing Settings > Type Categories. You will see your Type Categories listed. Click on "Edit" and check the box for Active. I am also including this KB solution on Type Categories - https://solutions.teamdynamix.com/TDClient/KB/A...
Upon making them active, you will see them on the drop down when creating a Ticket.
Please let me know if you have any additional questions.