fix: correct tool_choice dict format handling (fixes @ihower feedback)

Critical fix based on testing feedback from @ihower:
The previous fix assumed Responses Converter format (flat dict), but
LiteLLM uses ChatCompletions Converter which returns nested format.

Problem identified by @ihower:
- response_tool_choice was always "auto" even with specific tool names
- Root cause: Looking for wrong dict structure

Converter formats:
- ChatCompletions: {"type": "function", "function": {"name": "tool_name"}} ✅ (LiteLLM uses this)
- Responses: {"type": "function", "name": "tool_name"} ❌ (NOT used here)

Fix:
- Changed from tool_choice.get("name") to tool_choice.get("function").get("name")
- Added proper type checking for func_data dict
- Maintained all defensive checks (non-empty string, valid type, etc.)

Testing:
- Created comprehensive unit tests
- Created end-to-end flow tests
- All tests pass with nested dict format
- Verified: ModelSettings(tool_choice="my_tool") → ToolChoiceFunction(name="my_tool")

Generated with Lucas Wang<[email protected]>

Co-Authored-By: Claude <[email protected]>

Author: gn00295120

src/agents/extensions/models/litellm_model.py

@@ -377,16 +377,20 @@ async def _fetch_response(
             # Already a ToolChoiceFunction, use directly
             response_tool_choice = tool_choice
         elif isinstance(tool_choice, dict):
-            # Convert from Responses format dict to ToolChoiceFunction
-            # The Responses Converter returns: {"type": "function", "name": "tool_name"}
-            tool_name = tool_choice.get("name")
+            # Convert from ChatCompletions format dict to ToolChoiceFunction
+            # ChatCompletions Converter returns: {"type": "function", "function": {"name": "..."}}
+            func_data = tool_choice.get("function")
             if (
                 tool_choice.get("type") == "function"
-                and tool_name is not None
-                and isinstance(tool_name, str)
-                and tool_name  # Ensure non-empty string
+                and func_data is not None
+                and isinstance(func_data, dict)
             ):
-                response_tool_choice = ToolChoiceFunction(type="function", name=tool_name)
+                tool_name = func_data.get("name")
+                if isinstance(tool_name, str) and tool_name:  # Ensure non-empty string
+                    response_tool_choice = ToolChoiceFunction(type="function", name=tool_name)
+                else:
+                    # Fallback to auto if name is missing or invalid
+                    response_tool_choice = "auto"
             else:
                 # Fallback to auto if unexpected format
                 response_tool_choice = "auto"