feat: pass extra_body through to LiteLLM acompletion (#638)

**Purpose**  
Allow arbitrary `extra_body` parameters (e.g. `cached_content`) to be
forwarded into the LiteLLM call. Useful for context caching in Gemini
models
([docs](https://ai.google.dev/gemini-api/docs/caching?lang=python)).

**Example usage**  
```python
import os
from agents import Agent, ModelSettings
from agents.extensions.models.litellm_model import LitellmModel

cache_name = "cachedContents/34jopukfx5di"  # previously stored context

gemini_model = LitellmModel(
    model="gemini/gemini-1.5-flash-002",
    api_key=os.getenv("GOOGLE_API_KEY")
)

agent = Agent(
    name="Cached Gemini Agent",
    model=gemini_model,
    model_settings=ModelSettings(
        extra_body={"cached_content": cache_name}
    )
)

src/agents/extensions/models/litellm_model.py

@@ -269,6 +269,8 @@ class LitellmModel(Model):
             extra_kwargs["extra_query"] = model_settings.extra_query
         if model_settings.metadata:
             extra_kwargs["metadata"] = model_settings.metadata
+        if model_settings.extra_body and isinstance(model_settings.extra_body, dict):
+            extra_kwargs.update(model_settings.extra_body)
 
         ret = await litellm.acompletion(
             model=self.model,

tests/models/test_litellm_extra_body.py

@@ -0,0 +1,45 @@
+import litellm
+import pytest
+from litellm.types.utils import Choices, Message, ModelResponse, Usage
+
+from agents.extensions.models.litellm_model import LitellmModel
+from agents.model_settings import ModelSettings
+from agents.models.interface import ModelTracing
+
+
+@pytest.mark.allow_call_model_methods
+@pytest.mark.asyncio
+async def test_extra_body_is_forwarded(monkeypatch):
+    """
+    Forward `extra_body` entries into litellm.acompletion kwargs.
+
+    This ensures that user-provided parameters (e.g. cached_content)
+    arrive alongside default arguments.
+    """
+    captured: dict[str, object] = {}
+
+    async def fake_acompletion(model, messages=None, **kwargs):
+        captured.update(kwargs)
+        msg = Message(role="assistant", content="ok")
+        choice = Choices(index=0, message=msg)
+        return ModelResponse(choices=[choice], usage=Usage(0, 0, 0))
+
+    monkeypatch.setattr(litellm, "acompletion", fake_acompletion)
+    settings = ModelSettings(
+        temperature=0.1,
+        extra_body={"cached_content": "some_cache", "foo": 123}
+    )
+    model = LitellmModel(model="test-model")
+
+    await model.get_response(
+        system_instructions=None,
+        input=[],
+        model_settings=settings,
+        tools=[],
+        output_schema=None,
+        handoffs=[],
+        tracing=ModelTracing.DISABLED,
+        previous_response_id=None,
+    )
+
+    assert {"cached_content": "some_cache", "foo": 123}.items() <= captured.items()