fix: Stream errors as simple JSON objects in ADK web server SSE

The ADK web server's /run_sse endpoint now yields a JSON object like {"error": "..."} when an exception occurs during event generation. The adk_web_server_client is updated to detect this error payload and raise a RuntimeError.

Close #4291

Co-authored-by: George Weale <gweale@google.com>
PiperOrigin-RevId: 863475838

tests/unittests/cli/test_fast_api.py

@@ -1019,6 +1019,48 @@ def test_agent_run_sse_splits_artifact_delta(
   assert sse_events[1]["actions"]["artifactDelta"] == {"artifact.txt": 0}
 
 
+def test_agent_run_sse_yields_error_object_on_exception(
+    test_app, create_test_session, monkeypatch
+):
+  """Test /run_sse streams an error object if streaming raises."""
+  info = create_test_session
+
+  async def run_async_raises(
+      self,
+      *,
+      user_id: str,
+      session_id: str,
+      invocation_id: Optional[str] = None,
+      new_message: Optional[types.Content] = None,
+      state_delta: Optional[dict[str, Any]] = None,
+      run_config: Optional[RunConfig] = None,
+  ):
+    del user_id, session_id, invocation_id, new_message, state_delta, run_config
+    raise ValueError("boom")
+    if False:  # pylint: disable=using-constant-test
+      yield _event_1()
+
+  monkeypatch.setattr(Runner, "run_async", run_async_raises)
+
+  payload = {
+      "app_name": info["app_name"],
+      "user_id": info["user_id"],
+      "session_id": info["session_id"],
+      "new_message": {"role": "user", "parts": [{"text": "Hello agent"}]},
+      "streaming": True,
+  }
+
+  response = test_app.post("/run_sse", json=payload)
+  assert response.status_code == 200
+
+  sse_events = [
+      json.loads(line.removeprefix("data: "))
+      for line in response.text.splitlines()
+      if line.startswith("data: ")
+  ]
+  assert sse_events == [{"error": "boom"}]
+
+
 def test_list_artifact_names(test_app, create_test_session):
   """Test listing artifact names for a session."""
   info = create_test_session