fix: prefix OpenAI model with 'responses/' when thinking is enabled

- Add model prefixing to route OpenAI thinking requests to Responses API
- Fixes test failure where model should be 'responses/gpt-5.2' instead of 'gpt-5.2'
- Ensures OpenAI models with thinking parameter use Responses API for reasoning summary
- Prevents double-prefixing with existing 'responses/' check

litellm/llms/anthropic/experimental_pass_through/adapters/handler.py

@@ -64,7 +64,10 @@ class LiteLLMMessagesToCompletionTransformationHandler:
 
         model = completion_kwargs.get("model")
         if isinstance(model, str) and model and not model.startswith("responses/"):
-            reasoning_effort = completion_kwargs.get("reasoning_effort")
+            # Prefix model with "responses/" to route to OpenAI Responses API
+            completion_kwargs["model"] = f"responses/{model}"
+            
+        reasoning_effort = completion_kwargs.get("reasoning_effort")
         if isinstance(reasoning_effort, str) and reasoning_effort:
             completion_kwargs["reasoning_effort"] = {
                 "effort": reasoning_effort,