Python: fix(claude): preserve $defs in JSON schema for nested Pydantic models (#3655)

* fix(claude): preserve $defs in JSON schema for nested Pydantic models

- Preserve $defs section from Pydantic JSON schema when converting FunctionTool to SDK MCP tool
- This fixes tools with nested Pydantic models that use $ref references
- Add test for nested type schema preservation

Fixes #3654

* Adjust shared state import

* Fix MCP tool kwargs serialization bug

---------

Co-authored-by: Evan Mattson <evan.mattson@microsoft.com>

python/packages/claude/agent_framework_claude/_agent.py

@@ -511,6 +511,9 @@ class ClaudeAgent(BaseAgent, Generic[TOptions]):
             "properties": schema.get("properties", {}),
             "required": schema.get("required", []),
         }
+        # Preserve $defs for nested type references (Pydantic uses $defs for nested models)
+        if "$defs" in schema:
+            input_schema["$defs"] = schema["$defs"]
 
         return SdkMcpTool(
             name=func_tool.name,

python/packages/claude/tests/test_claude_agent.py

@@ -499,6 +499,33 @@ class TestClaudeAgentToolConversion:
         assert sdk_tool.input_schema is not None
         assert "properties" in sdk_tool.input_schema  # type: ignore[operator]
 
+    def test_function_tool_to_sdk_mcp_tool_preserves_defs_for_nested_types(self) -> None:
+        """Test that $defs is preserved for tools with nested Pydantic models."""
+        from pydantic import BaseModel
+
+        class Address(BaseModel):
+            street: str
+            city: str
+
+        class Person(BaseModel):
+            name: str
+            address: Address
+
+        @tool
+        def create_person(person: Person) -> str:
+            """Create a person with address."""
+            return f"{person.name} lives at {person.address.street}, {person.address.city}"
+
+        agent = ClaudeAgent()
+        sdk_tool = agent._function_tool_to_sdk_mcp_tool(create_person)  # type: ignore[reportPrivateUsage]
+
+        # Verify $defs is preserved in the schema
+        assert sdk_tool.input_schema is not None
+        assert "$defs" in sdk_tool.input_schema  # type: ignore[operator]
+        assert "Address" in sdk_tool.input_schema["$defs"]  # type: ignore[index]
+        # Verify the nested reference exists in properties
+        assert "person" in sdk_tool.input_schema["properties"]  # type: ignore[index]
+
     async def test_tool_handler_success(self) -> None:
         """Test tool handler executes successfully."""