Hello @Kayla_Bayens! While you are able to configure a Task Template in a Project Template, they indeed are not supported at this current time.
Task templates don’t currently copy over when you duplicate projects. This applies to creating a project from a Project Template as well. This is something Asana is aware of and I’m certain they are working hard to change this behavior.
In the meantime, be sure to upvote this post: Task Templates Within Project Templates