Presently, you can assign a task group without setting up an automation rule, and "assign" the task to a specific individual.

For Anniversaries (or Birthdays), it would be helpful to assign the task to a specific group (i.e. the Manager (and even indirect Manager)). Managers can change over the course of the year, so assigning it to an individual risks losing the task if the person offboards. If the task is attached to the "manager" role, however, it could stay active, regardless of who is in the seat.