[CRITICAL] POST /supervisors/{type}/execute triggers real multi-worker LLM execution with no authentication

[jsogarro]

[CRITICAL] Unauthenticated supervisor execution endpoint

Summary
POST /api/v1/supervisors/{supervisor_type}/execute runs a hierarchical supervisor that coordinates multiple worker agents (real LLM calls) and declares no authentication dependency — any caller can trigger arbitrary, cost-incurring agent execution.

Evidence
src/api/routes/supervisor_api.py:86-93

@router.post("/{supervisor_type}/execute", response_model=SupervisorExecuteResponse)
async def execute_supervisor_task(
    supervisor_type: SupervisorType,
    request: SupervisorExecuteRequest,
    service: SupervisorCoordinationService = _SUPERVISOR_SERVICE_DEPENDENCY,
) -> SupervisorExecuteResponse:

The only dependency is the supervisor service itself; there is no identity check and no authority-reference gate (unlike the agent-execution endpoints, which at least require a client-supplied authority reference).

Failure scenario: an unauthenticated POST to /api/v1/supervisors/{supervisor_type}/execute with an arbitrary task payload runs the full supervisor→worker pipeline, incurring real LLM cost and consuming any downstream resources the supervisor touches.

Impact
Unauthenticated, unbounded triggering of expensive multi-agent LLM execution — a direct cost/DoS vector and a bypass of whatever authorization model the rest of the agent-execution API expects.

Remediation
Add an authentication dependency and, ideally, the same authority-reference gating pattern used in agent_api.py. Add a regression test asserting 401/403 for an unauthenticated request.

Acceptance

uv run pytest tests/test_supervisor_api.py -v