fix: apply black formatting to responses/main.py and clarify branch order in transformation.py

- Fix black formatting violations in litellm/responses/main.py (parenthesized
  type annotation style)
- Add comment explaining intentional branch order in get_complete_url():
  /projects/ must be checked before the general services.ai.azure.com path
  because project-based endpoints use /openai/v1/responses rather than
  /models/responses

litellm/llms/azure_ai/responses/transformation.py

@@ -113,7 +113,10 @@ class AzureAIResponsesAPIConfig(OpenAIResponsesAPIConfig):
         if "api-version" not in query_params and api_version:
             query_params["api-version"] = api_version
 
-        # Build the responses endpoint path
+        # Build the responses endpoint path.
+        # Check /projects/ first: project-based endpoints under
+        # services.ai.azure.com need /openai/v1/responses, which differs
+        # from the non-project services.ai.azure.com path (/models/responses).
         if "/projects/" in api_base:
             new_url = _add_path_to_api_base(
                 api_base=api_base, ending_path="/openai/v1/responses"

litellm/responses/main.py

@@ -1115,11 +1115,11 @@ def delete_responses(
             raise ValueError("custom_llm_provider is required but passed as None")
 
         # get provider config
-        responses_api_provider_config: Optional[
-            BaseResponsesAPIConfig
-        ] = ProviderConfigManager.get_provider_responses_api_config(
-            model=None,
-            provider=custom_llm_provider,
+        responses_api_provider_config: Optional[BaseResponsesAPIConfig] = (
+            ProviderConfigManager.get_provider_responses_api_config(
+                model=None,
+                provider=custom_llm_provider,
+            )
         )
 
         if responses_api_provider_config is None:
@@ -1296,11 +1296,11 @@ def get_responses(
             raise ValueError("custom_llm_provider is required but passed as None")
 
         # get provider config
-        responses_api_provider_config: Optional[
-            BaseResponsesAPIConfig
-        ] = ProviderConfigManager.get_provider_responses_api_config(
-            model=None,
-            provider=custom_llm_provider,
+        responses_api_provider_config: Optional[BaseResponsesAPIConfig] = (
+            ProviderConfigManager.get_provider_responses_api_config(
+                model=None,
+                provider=custom_llm_provider,
+            )
         )
 
         if responses_api_provider_config is None:
@@ -1454,11 +1454,11 @@ def list_input_items(
         if custom_llm_provider is None:
             raise ValueError("custom_llm_provider is required but passed as None")
 
-        responses_api_provider_config: Optional[
-            BaseResponsesAPIConfig
-        ] = ProviderConfigManager.get_provider_responses_api_config(
-            model=None,
-            provider=custom_llm_provider,
+        responses_api_provider_config: Optional[BaseResponsesAPIConfig] = (
+            ProviderConfigManager.get_provider_responses_api_config(
+                model=None,
+                provider=custom_llm_provider,
+            )
         )
 
         if responses_api_provider_config is None:
@@ -1613,11 +1613,11 @@ def cancel_responses(
             raise ValueError("custom_llm_provider is required but passed as None")
 
         # get provider config
-        responses_api_provider_config: Optional[
-            BaseResponsesAPIConfig
-        ] = ProviderConfigManager.get_provider_responses_api_config(
-            model=None,
-            provider=custom_llm_provider,
+        responses_api_provider_config: Optional[BaseResponsesAPIConfig] = (
+            ProviderConfigManager.get_provider_responses_api_config(
+                model=None,
+                provider=custom_llm_provider,
+            )
         )
 
         if responses_api_provider_config is None:
@@ -1801,11 +1801,11 @@ def compact_responses(
             raise ValueError("custom_llm_provider is required but passed as None")
 
         # get provider config
-        responses_api_provider_config: Optional[
-            BaseResponsesAPIConfig
-        ] = ProviderConfigManager.get_provider_responses_api_config(
-            model=model,
-            provider=custom_llm_provider,
+        responses_api_provider_config: Optional[BaseResponsesAPIConfig] = (
+            ProviderConfigManager.get_provider_responses_api_config(
+                model=model,
+                provider=custom_llm_provider,
+            )
         )
 
         if responses_api_provider_config is None: