feat: add Gemini 3.1 Flash Live support for run_live()

Changes:
1. send_realtime(): use audio= instead of deprecated media= (all models)
2. send_content(): use send_tool_response() for function responses (all models)
3. send_content(): route text via send_realtime_input for 3.1 models
4. connect(): inject history_config for 3.1 models

Changes 1-2 are backward-compatible API upgrades (removing deprecated usage).
Changes 3-4 are conditional on model version containing '3.1'.

Tested in production with real phone calls on gemini-3.1-flash-live-preview.

Note: 3.1 models do not support enable_affective_dialog,
context_window_compression, or proactivity config fields.
These are documented in issue #5075 as model limitations.

Fixes #5018

Author: imazizongit

src/google/adk/models/gemini_llm_connection.py

@@ -105,12 +105,21 @@ async def send_content(self, content: types.Content):
       # All parts have to be function responses.
       function_responses = [part.function_response for part in content.parts]
       logger.debug('Sending LLM function response: %s', function_responses)
-      await self._gemini_session.send(
-          input=types.LiveClientToolResponse(
-              function_responses=function_responses
-          ),
+      await self._gemini_session.send_tool_response(
+          function_responses=function_responses
       )
     else:
+      # 3.1 models reject LiveClientContent for mid-conversation text
+      if self._model_version and '3.1' in self._model_version:
+        text_parts = [p.text for p in content.parts if p.text]
+        if text_parts:
+          combined = ' '.join(text_parts)
+          logger.debug(
+              'Sending text via realtime input for 3.1 model: %s',
+              combined[:100],
+          )
+          await self._gemini_session.send_realtime_input(text=combined)
+          return
       logger.debug('Sending LLM new content %s', content)
       await self._gemini_session.send(
           input=types.LiveClientContent(
@@ -128,7 +137,7 @@ async def send_realtime(self, input: RealtimeInput):
     if isinstance(input, types.Blob):
       # The blob is binary and is very large. So let's not log it.
       logger.debug('Sending LLM Blob.')
-      await self._gemini_session.send_realtime_input(media=input)
+      await self._gemini_session.send_realtime_input(audio=input)
 
     elif isinstance(input, types.ActivityStart):
       logger.debug('Sending LLM activity start signal.')

src/google/adk/models/google_llm.py

@@ -401,6 +401,16 @@ async def connect(self, llm_request: LlmRequest) -> BaseLlmConnection:
             ' backend. Please use Vertex AI backend.'
         )
     llm_request.live_connect_config.tools = llm_request.config.tools
+
+    # 3.1 models require history_config for session history to work
+    model_name = llm_request.model or ''
+    if '3.1' in model_name and not getattr(
+        llm_request.live_connect_config, 'history_config', None
+    ):
+      llm_request.live_connect_config.history_config = types.HistoryConfig(
+          initial_history_in_client_content=True
+      )
+
     logger.debug('Connecting to live with llm_request:%s', llm_request)
     logger.debug('Live connect config: %s', llm_request.live_connect_config)
     async with self._live_api_client.aio.live.connect(