The requirement describes a standard vertical access pattern that is best handled by the Role Hierarchy (Option C).

In Salesforce, when the Organization-Wide Default (OWD) for an object (like Case) is set to Private, the Role Hierarchy provides the following functionality by default:

Managers see subordinates' data: Users placed higher in the hierarchy automatically gain access to records owned by or shared with users below them. By placing support managers at the top of the hierarchy, they will be able to see all cases owned by the agents.

Agents see restricted data: Agents will only see the records they own or those shared with them. The requirement that they see cases owned by "someone in their role or a subordinate role" is exactly how the hierarchy facilitates vertical data flow.

While Criteria-based sharing rules (Option D) could potentially share cases with managers, it would be much harder to manage the "subordinate" logic dynamically as the team grows. Sharing Sets (Option A) are specifically for Experience Cloud (External) users and do not apply to internal support staff. Apex Managed Sharing (Option B) is a "last resort" for complex, programmatic sharing logic that cannot be achieved via declarative tools. Since the requirement aligns perfectly with the standard manager-subordinate relationship, the Role Hierarchy is the most efficient and standard solution.