chore(deploy): add production caddy setup

tests/test_demo_app.py

@@ -105,6 +105,16 @@ def test_demo_auth_flow_forwards_to_grpc_client() -> None:
         app.dependency_overrides.clear()
 
 
+def test_healthz() -> None:
+    client = TestClient(app)
+    try:
+        response = client.get("/healthz")
+        assert response.status_code == 200
+        assert response.json() == {"status": "ok"}
+    finally:
+        client.close()
+
+
 def test_debug_otp_endpoint_reads_redis_when_enabled() -> None:
     app.dependency_overrides[get_app_settings] = lambda: Settings(demo_enable_debug_otp=True)
     app.dependency_overrides[get_debug_redis] = lambda: FakeDebugRedis()