Health Check

Return a lightweight service health and active-session snapshot.

Args: None.

Returns: A healthy status string and the current number of registered sessions.

Raises: None.

Behavior: The endpoint reads only the in-memory registry and does not expire sessions, await solver work, or probe Z3. It therefore confirms process responsiveness rather than the satisfiability or completion of individual requests.

HealthCheck(status="healthy", active_sessions=0)