You're creating a new entity-backed record type without data sync enabled.

Grant Viewer permissions to the underlying interface object for the Summary view.

Add the "ACME Supervisors" group as a member of the "Database Editors" group and grant DELETE privileges.

Update the record action security for "Delete Case" and include the "ACME Supervisors" group within the visibility settings.

Add the "ACME Supervisors" group as a Viewer to the data store mapped to the record.