Fix: Add shared_session support for embedding calls with connection pooling

The shared_session parameter was not being properly handled in embedding calls,
causing it to be passed through to provider API requests where it's not needed.

Changes:
- Added shared_session to all_litellm_params to filter it from provider API request body
- Extract shared_session in main embedding() function and pass it explicitly
- Updated OpenAI embedding handlers (embedding() and aembedding()) to accept shared_session
- Pass shared_session to _get_openai_client for HTTP client creation

This enables proper connection pooling for embedding requests when shared_session
is provided, improving performance for high-throughput scenarios.

litellm/llms/openai/openai.py

@@ -1125,6 +1125,7 @@ class OpenAIChatCompletion(BaseLLM, BaseOpenAILLM):
         api_base: Optional[str] = None,
         client: Optional[AsyncOpenAI] = None,
         max_retries=None,
+        shared_session: Optional["ClientSession"] = None,
     ):
         try:
             openai_aclient: AsyncOpenAI = self._get_openai_client(  # type: ignore
@@ -1134,6 +1135,7 @@ class OpenAIChatCompletion(BaseLLM, BaseOpenAILLM):
                 timeout=timeout,
                 max_retries=max_retries,
                 client=client,
+                shared_session=shared_session,
             )
             headers, response = await self.make_openai_embedding_request(
                 openai_aclient=openai_aclient,
@@ -1197,6 +1199,7 @@ class OpenAIChatCompletion(BaseLLM, BaseOpenAILLM):
         client=None,
         aembedding=None,
         max_retries: Optional[int] = None,
+        shared_session: Optional["ClientSession"] = None,
     ) -> EmbeddingResponse:
         super().embedding()
         try:
@@ -1223,6 +1226,7 @@ class OpenAIChatCompletion(BaseLLM, BaseOpenAILLM):
                     timeout=timeout,
                     client=client,
                     max_retries=max_retries,
+                    shared_session=shared_session,
                 )
 
             openai_client: OpenAI = self._get_openai_client(  # type: ignore

litellm/main.py

@@ -3969,6 +3969,7 @@ def embedding(  # noqa: PLR0915
     """
     azure = kwargs.get("azure", None)
     client = kwargs.pop("client", None)
+    shared_session = kwargs.get("shared_session", None)
     max_retries = kwargs.get("max_retries", None)
     litellm_logging_obj: LiteLLMLoggingObj = kwargs.get("litellm_logging_obj")  # type: ignore
     mock_response: Optional[List[float]] = kwargs.get("mock_response", None)  # type: ignore
@@ -4158,6 +4159,7 @@ def embedding(  # noqa: PLR0915
                 client=client,
                 aembedding=aembedding,
                 max_retries=max_retries,
+                shared_session=shared_session,
             )
         elif custom_llm_provider == "databricks":
             api_base = api_base or litellm.api_base or get_secret("DATABRICKS_API_BASE")  # type: ignore