Not all employees will attend to Talent ESS on a regular basis. As they can be notified in email of assigned work items, it should be possible to notify of assigned checklist tasks as well. Both when they first get assigned, if a task is re-assigned and if a task becomes overdue.
The task assignee should be notified. If a task is assigned to a group, all members of the group should be notified.
Today it is not possible to build your own flow for notifications: checklist tasks are not in CDS. And only onboarding tasks have a DMF data entity, not transition an offboarding tasks.