core[patch]: add additionalProperties recursively to oai function if strict (#25169)

Hello. 
First of all, thank you for maintaining such a great project.

## Description
In https://github.com/langchain-ai/langchain/pull/25123, support for
structured_output is added. However, `"additionalProperties": false`
needs to be included at all levels when a nested object is generated.

error from current code:
https://gist.github.com/fufufukakaka/e9b475300e6934853d119428e390f204
```
BadRequestError: Error code: 400 - {'error': {'message': "Invalid schema for response_format 'JokeWithEvaluation': In context=('properties', 'self_evaluation'), 'additionalProperties' is required to be supplied and to be false", 'type': 'invalid_request_error', 'param': 'response_format', 'code': None}}
```

Reference: [Introducing Structured Outputs in the
API](https://openai.com/index/introducing-structured-outputs-in-the-api/)

```json
{
  "model": "gpt-4o-2024-08-06",
  "messages": [
    {
      "role": "system",
      "content": "You are a helpful math tutor."
    },
    {
      "role": "user",
      "content": "solve 8x + 31 = 2"
    }
  ],
  "response_format": {
    "type": "json_schema",
    "json_schema": {
      "name": "math_response",
      "strict": true,
      "schema": {
        "type": "object",
        "properties": {
          "steps": {
            "type": "array",
            "items": {
              "type": "object",
              "properties": {
                "explanation": {
                  "type": "string"
                },
                "output": {
                  "type": "string"
                }
              },
              "required": ["explanation", "output"],
              "additionalProperties": false
            }
          },
          "final_answer": {
            "type": "string"
          }
        },
        "required": ["steps", "final_answer"],
        "additionalProperties": false
      }
    }
  }
}
```

In the current code, `"additionalProperties": false` is only added at
the last level.
This PR introduces the `_add_additional_properties_key` function, which
recursively adds `"additionalProperties": false` to the entire JSON
schema for the request.

Twitter handle: `@fukkaa1225`

Thank you!

---------

Co-authored-by: Bagatur <baskaryan@gmail.com>

libs/partners/openai/tests/integration_tests/chat_models/test_base.py

@@ -868,6 +868,43 @@ def test_structured_output_strict(
         next(chat.stream("Tell me a joke about cats."))
 
 
+@pytest.mark.parametrize(
+    ("model", "method", "strict"), [("gpt-4o-2024-08-06", "json_schema", None)]
+)
+def test_nested_structured_output_strict(
+    model: str, method: Literal["json_schema"], strict: Optional[bool]
+) -> None:
+    """Test to verify structured output with strict=True for nested object."""
+
+    from typing import TypedDict
+
+    llm = ChatOpenAI(model=model, temperature=0)
+
+    class SelfEvaluation(TypedDict):
+        score: int
+        text: str
+
+    class JokeWithEvaluation(TypedDict):
+        """Joke to tell user."""
+
+        setup: str
+        punchline: str
+        self_evaluation: SelfEvaluation
+
+    # Schema
+    chat = llm.with_structured_output(JokeWithEvaluation, method=method, strict=strict)
+    result = chat.invoke("Tell me a joke about cats.")
+    assert isinstance(result, dict)
+    assert set(result.keys()) == {"setup", "punchline", "self_evaluation"}
+    assert set(result["self_evaluation"].keys()) == {"score", "text"}
+
+    for chunk in chat.stream("Tell me a joke about cats."):
+        assert isinstance(chunk, dict)
+    assert isinstance(chunk, dict)  # for mypy
+    assert set(chunk.keys()) == {"setup", "punchline", "self_evaluation"}
+    assert set(chunk["self_evaluation"].keys()) == {"score", "text"}
+
+
 def test_json_mode() -> None:
     llm = ChatOpenAI(model="gpt-4o-mini", temperature=0)
     response = llm.invoke(