fix: address PR review feedback — F821, double auth, strict field, docs format, system-only fallback

- Fix F821: add BaseTokenCounter TYPE_CHECKING import in gpt_transformation.py
- Remove duplicate auth invocation in count_response_input_tokens endpoint
- Preserve `strict` field during chat→Responses API tool conversion
- Fix docs tools example to use chat completions format (not Responses API format)
- Return None early for system-only messages to avoid noisy error logs

docs/my-website/docs/count_tokens.md

@@ -65,11 +65,13 @@ async def main():
         messages=[{"role": "user", "content": "What's the weather in Paris?"}],
         tools=[{
             "type": "function",
-            "name": "get_weather",
-            "description": "Get weather for a city",
-            "parameters": {
-                "type": "object",
-                "properties": {"city": {"type": "string"}},
+            "function": {
+                "name": "get_weather",
+                "description": "Get weather for a city",
+                "parameters": {
+                    "type": "object",
+                    "properties": {"city": {"type": "string"}},
+                },
             },
         }],
         system="You are a helpful weather assistant.",

litellm/llms/openai/chat/gpt_transformation.py

@@ -58,6 +58,7 @@ from ..common_utils import OpenAIError
 
 if TYPE_CHECKING:
     from litellm.litellm_core_utils.litellm_logging import Logging as _LiteLLMLoggingObj
+    from litellm.llms.base_llm.base_utils import BaseTokenCounter
     from litellm.types.llms.openai import ChatCompletionToolParam
 
     LiteLLMLoggingObj = _LiteLLMLoggingObj

litellm/llms/openai/responses/count_tokens/token_counter.py

@@ -68,6 +68,10 @@ class OpenAITokenCounter(BaseTokenCounter):
         if instructions is None and system is not None:
             instructions = system if isinstance(system, str) else str(system)
 
+        # If no input items were produced (e.g., system-only messages), fall back to local counting
+        if not input_items:
+            return None
+
         try:
             result = await openai_count_tokens_handler.handle_count_tokens_request(
                 model=model_to_use,

litellm/llms/openai/responses/count_tokens/transformation.py

@@ -75,12 +75,15 @@ class OpenAICountTokensConfig:
         for tool in tools:
             if tool.get("type") == "function" and "function" in tool:
                 func = tool["function"]
-                transformed.append({
+                item: Dict[str, Any] = {
                     "type": "function",
                     "name": func.get("name", ""),
                     "description": func.get("description", ""),
                     "parameters": func.get("parameters", {}),
-                })
+                }
+                if "strict" in func:
+                    item["strict"] = func["strict"]
+                transformed.append(item)
             else:
                 # Pass through non-function tools (e.g., web_search, file_search)
                 transformed.append(tool)

litellm/proxy/response_api_endpoints/endpoints.py

@@ -417,7 +417,6 @@ async def cursor_chat_completions(
 )
 async def count_response_input_tokens(
     request: Request,
-    user_api_key_dict: UserAPIKeyAuth = Depends(user_api_key_auth),
 ):
     """
     Count input tokens for OpenAI Responses API format.