fix(live): history_config rejection on Vertex/Enterprise Live sessions

Merge google#6035

**Please ensure you have read the [contribution guide](https://github.com/google/adk-python/blob/main/CONTRIBUTING.md) before creating a pull request.**

### Link to Issue or Description of Change

**Problem:**
On the Vertex AI / Gemini Enterprise Agent Platform backend, ADK auto-injects `history_config` into the Live setup message when seeding conversation history. That backend has no `history_config` field and rejects it with `ValueError: history_config parameter is only supported in Gemini Developer API mode, not in Gemini Enterprise Agent Platform mode`

**Solution:**
Gate the history_config auto-injection to the Gemini Developer API backend only (`isinstance(llm, Gemini)` and `llm._api_backend == GoogleLLMVariant.GEMINI_API`). On Vertex, history is already seeded via the sanctioned `send_history` (`send_client_content`) path.

### Testing Plan

**Unit Tests:**

- [X] I have added or updated unit tests for my change.
- [X] All unit tests pass locally.

$ pytest tests/unittests/flows/llm_flows/test_base_llm_flow.py -k history_config
2 passed, 35 deselected, 4 warnings in 0.78s

**Manual End-to-End (E2E) Tests:**

Verified intended functionality in ADK web.

### Checklist

- [X] I have read the [CONTRIBUTING.md](https://github.com/google/adk-python/blob/main/CONTRIBUTING.md) document.
- [X] I have performed a self-review of my own code.
- [X] I have commented my code, particularly in hard-to-understand areas.
- [X] I have added tests that prove my fix is effective or that my feature works.
- [X] New and existing unit tests pass locally with my changes.
- [X] I have manually tested my changes end-to-end.
- [X] Any dependent changes have been merged and published in downstream modules.

### Additional context

N/A

COPYBARA_INTEGRATE_REVIEW=google#6035 from allen-stephen:fix/live-history-config-bug cf8e1fc
PiperOrigin-RevId: 933402607

Author: allen-stephen

src/google/adk/flows/llm_flows/base_llm_flow.py

@@ -555,9 +555,18 @@ async def run_live(
         # initial_history_in_client_content to True. This tells the Live server
         # that the provided history already includes the model's past responses,
         # preventing the server from generating duplicate responses for those replayed turns.
+        #
+        # ``history_config`` is only supported by the Gemini Developer API
+        # backend; the Vertex AI / Gemini Enterprise Agent Platform backend has
+        # no such field on its live setup message and rejects it. On Vertex,
+        # history is instead seeded by ``send_history`` below
+        # (``send_client_content`` with prior turns), so we skip
+        # ``history_config`` for that backend.
         if (
             llm_request.contents
             and not invocation_context.live_session_resumption_handle
+            and isinstance(llm, Gemini)
+            and llm._api_backend == GoogleLLMVariant.GEMINI_API  # pylint: disable=protected-access
         ):
           if not llm_request.live_connect_config:
             llm_request.live_connect_config = types.LiveConnectConfig()

tests/unittests/flows/llm_flows/test_base_llm_flow.py

@@ -1402,15 +1402,8 @@ async def mock_receive_2():
 
 
 @pytest.mark.asyncio
-@pytest.mark.parametrize(
-    'api_backend',
-    [
-        GoogleLLMVariant.GEMINI_API,
-        GoogleLLMVariant.VERTEX_AI,
-    ],
-)
-async def test_run_live_history_config_set_for_all_backends(api_backend):
-  """Test that run_live sets history_config for all backends."""
+async def test_run_live_history_config_set_for_gemini_api_backend():
+  """history_config is auto-set when seeding history on the Gemini API backend."""
 
   real_model = Gemini(model='gemini-3.1-flash-live-preview')
   mock_connection = mock.AsyncMock()
@@ -1457,7 +1450,7 @@ async def mock_receive():
             Gemini,
             '_api_backend',
             new_callable=mock.PropertyMock,
-            return_value=api_backend,
+            return_value=GoogleLLMVariant.GEMINI_API,
         ):
           try:
             async for _ in flow.run_live(invocation_context):
@@ -1475,6 +1468,75 @@ async def mock_receive():
           )
 
 
+@pytest.mark.asyncio
+async def test_run_live_history_config_not_set_for_vertex_backend():
+  """history_config is NOT auto-set on the Vertex backend (it rejects it).
+
+  The Vertex AI / Gemini Enterprise Agent Platform live setup message has no
+  ``history``/``history_config`` field. ADK seeds Vertex history via
+  ``send_history`` (``send_client_content``) instead, so the auto-injection of
+  ``history_config`` must be skipped for this backend.
+  """
+
+  real_model = Gemini(model='gemini-3.1-flash-live-preview')
+  mock_connection = mock.AsyncMock()
+
+  class StopTestError(Exception):
+    pass
+
+  async def mock_receive():
+    yield LlmResponse(
+        content=types.Content(parts=[types.Part.from_text(text='hi')])
+    )
+    raise StopTestError('stop')
+
+  mock_connection.receive = mock.Mock(side_effect=mock_receive)
+
+  agent = Agent(name='test_agent', model=real_model)
+  invocation_context = await testing_utils.create_invocation_context(
+      agent=agent
+  )
+  invocation_context.live_request_queue = LiveRequestQueue()
+
+  flow = BaseLlmFlowForTesting()
+
+  with mock.patch.object(flow, '_send_to_model', new_callable=AsyncMock):
+
+    async def mock_preprocess(ctx, req):
+      req.contents = [
+          types.Content(parts=[types.Part.from_text(text='history')])
+      ]
+      yield Event(id=Event.new_id(), author='test')
+
+    with mock.patch.object(
+        flow, '_preprocess_async', side_effect=mock_preprocess
+    ):
+      with mock.patch.object(
+          Gemini, '_api_backend', new_callable=mock.PropertyMock
+      ) as mock_backend:
+        mock_backend.return_value = GoogleLLMVariant.VERTEX_AI
+        with mock.patch(
+            'google.adk.models.google_llm.Gemini.connect'
+        ) as mock_connect:
+          mock_connect.return_value.__aenter__.return_value = mock_connection
+
+          try:
+            async for _ in flow.run_live(invocation_context):
+              pass
+          except StopTestError:
+            pass
+
+          assert mock_connect.call_count == 1
+          called_req = mock_connect.call_args[0][0]
+          # history_config must NOT be auto-injected on Vertex.
+          assert (
+              called_req.live_connect_config is None
+              or called_req.live_connect_config.history_config is None
+          )
+          # History is still seeded via send_history (send_client_content).
+          mock_connection.send_history.assert_awaited_once()
+
+
 @pytest.mark.asyncio
 async def test_run_live_respects_explicit_initial_history_in_client_content_false():
   """Test that run_live respects explicit initial_history_in_client_content=False in RunConfig."""