[Bug]: Tool signature error for Anthropic when tool parameter includes a class

[jk10001]

Describe the bug

With anthropic models there is an issue with the tool signature if the function registered has a parameter that is defined by a class.

The code below results in the error:
anthropic.BadRequestError: Error code: 400 - {'type': 'error', 'error': {'type': 'invalid_request_error', 'message': 'tools.1.custom.input_schema: JSON schema is invalid. It must match JSON Schema draft 2020-12 (https://json-schema.org/draft/2020-12). Learn more about tool use at https://docs.anthropic.com/en/docs/tool-use.'}}

Steps to reproduce

Code below produces the error. Replace config_claude_haiku_35 with your config.

from autogen import register_function
from typing import List, TypedDict
import os
from autogen import ConversableAgent
import pprint
from dotenv import load_dotenv
import json


class class_test(TypedDict):
    item1: str
    item2: str


def tool_call_test(information: str, class_test_list: List[class_test]) -> str:
    return "TERMINATE"


assistant = ConversableAgent(
    name="Assistant",
    system_message="You are a helpful AI assistant. "
    "Return 'TERMINATE' when the task is done.",
    llm_config={
        "cache_seed": False,
        "config_list": config_claude_haiku_35,
    },
)


user_proxy = ConversableAgent(
    name="User",
    llm_config={
        "cache_seed": False,
    },
    human_input_mode="ALWAYS",
)


register_function(
    tool_call_test,
    caller=assistant,
    executor=user_proxy,
    name="tool_call_test",
    description="A function to add record some information.",
)

pprint.pprint(assistant.llm_config["tools"])

message1 = "Make a call to tool_call_test. Make up the data."

chat_result = user_proxy.initiate_chat(assistant, message=message1)
`

The tool signature that is registered automatically is:
`
[
    {
        "type": "function",
        "function": {
            "description": "A function to add record some information.",
            "name": "tool_call_test",
            "parameters": {
                "type": "object",
                "properties": {
                    "information": {
                        "type": "string",
                        "description": "information"
                    },
                    "class_test_list": {
                        "$defs": {
                            "class_test": {
                                "properties": {
                                    "item1": {
                                        "title": "Item1",
                                        "type": "string"
                                    },
                                    "item2": {
                                        "title": "Item2",
                                        "type": "string"
                                    }
                                },
                                "required": [
                                    "item1",
                                    "item2"
                                ],
                                "title": "class_test",
                                "type": "object"
                            }
                        },
                        "items": {
                            "$ref": "#/$defs/class_test"
                        },
                        "type": "array",
                        "description": "class_test_list"
                    }
                },
                "required": [
                    "information",
                    "class_test_list"
                ]
            }
        }
    }
]

The error is caused by
"$ref": "#/$defs/class_test".
If you manually change the tool signature with update_tool_signature so this is
"$ref": "#/properties/class_test_list/$defs/class_test"
Claude uses the function correctly.

Other LLMs (e.g. llama-3.3-70b) seem to be able to use the tool correctly with either tool signature.

Model Used

Claude Haiku 3.5, Sonnet 3.5

Expected Behavior

No response

Screenshots and logs

No response

Additional Information

No response