Health check (GET /api/health)
Always-on endpoint (no auth, no flag required) for use with container probes and load balancers. Returns 200 OK or 503 Service Unavailable with a JSON body indicating the status of three subsystems:

• sqlite — connectivity check via SELECT 1 on the search DB
• data_dir — storage directory accessibility
• search — background indexing goroutine state (ok / indexing / failed)