OK, so there's an additional paid plugin named Customer Service Case Action Status that adds the action_status integer type column to the task table, with 4 choices for task and the same 4 choices for sn_customerservice_case. They could/should have mentioned all of this in the documentation.
This field is affected by these flows:
Set Needs Attention if additional comments are added by others
Create blocked by record if case needs customer information
Create blocked by record if Case Task is associated with case
Created blocked by record if Problem is associated with case
Update case when blocked by record is created
Resolve blocked by record if Case Task is closed
Resolve blocked by record if Problem is closed or Fix is communicated
Resolve blocked by record if Problem is closed or Fix/Workaround is communicated
Resolve blocked by record if user information is provided for case
You can also affect this field directly by adding the Needs attention field to your form. Checking or Unchecking this box (either manually or from one of the other Flows) runs the Flow named Update case when Needs attention field is toggled, which just runs the Subflow named Update Case for action status, which is where the real works happens.
There's also this bit of documentation if you haven't seen it
https://docs.servicenow.com/bundle/quebec-customer-service-management/page/product/customer-service-...
