fix: resolve Greptile P0 issues for GitHub Copilot premium billing

This commit addresses both P0 issues flagged in Greptile review to achieve
5/5 score (currently 4/5).

**P0 Issue #1: Responses API X-Initiator never set**

Root cause: The X-Initiator header was being set in validate_environment(),
which doesn't have access to the `input` parameter. The _get_input_from_params()
helper checked for `litellm_params.input`, but this attribute doesn't exist in
GenericLiteLLMParams - the `input` parameter is passed separately to
transform_responses_api_request().

Fix: Moved X-Initiator and vision header logic from validate_environment() to
transform_responses_api_request() where the `input` parameter is available.
This ensures the header is correctly set for Responses API requests.

Changes:
- Added transform_responses_api_request() override in
  GithubCopilotResponsesAPIConfig that:
  1. Calculates X-Initiator based on input analysis
  2. Adds copilot-vision-request header if images detected
  3. Calls parent to validate input and handle reasoning items
- Removed broken _get_input_from_params() helper
- Simplified validate_environment() docstring and removed duplicate logic

**P0 Issue #2: Integration test in wrong location**

Root cause: tests/llm_translation/test_github_copilot_billing.py makes real
network calls via litellm.completion(), violating the repository rule that
tests/llm_translation/ is for mock-only tests.

Fix: Moved test file to tests/llm_responses_api_testing/ which is the
designated directory for integration tests that make real API calls.

Impact:
- Responses API requests now correctly set X-Initiator header
- Multi-turn agentic workflows (Plan mode, tool calls, agent flows) will
  only consume 1 premium request per session instead of 1 per turn
- Integration tests now in proper location per repository conventions

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

litellm/llms/github_copilot/responses/transformation.py

@@ -88,6 +88,44 @@ class GithubCopilotResponsesAPIConfig(OpenAIResponsesAPIConfig):
         """
         return dict(response_api_optional_params)
 
+    def transform_responses_api_request(
+        self,
+        model: str,
+        input: Union[str, ResponseInputParam],
+        response_api_optional_request_params: Dict,
+        litellm_params: GenericLiteLLMParams,
+        headers: dict,
+    ) -> Dict:
+        """
+        Transform the Responses API request and set X-Initiator header.
+
+        GitHub Copilot requires X-Initiator header based on input analysis.
+        This is set here (not in validate_environment) because only this method
+        has access to the input parameter.
+        """
+        # Add X-Initiator header based on input analysis
+        initiator = self._get_initiator(input)
+        headers["X-Initiator"] = initiator
+        verbose_logger.debug(
+            f"GitHub Copilot Responses API: Set X-Initiator={initiator}"
+        )
+
+        # Add vision header if input contains images
+        if self._has_vision_input(input):
+            headers["copilot-vision-request"] = "true"
+            verbose_logger.debug(
+                "GitHub Copilot Responses API: Enabled vision request"
+            )
+
+        # Call parent to get request body (validates input, handles reasoning items)
+        return super().transform_responses_api_request(
+            model=model,
+            input=input,
+            response_api_optional_request_params=response_api_optional_request_params,
+            litellm_params=litellm_params,
+            headers=headers,
+        )
+
     def validate_environment(
         self,
         headers: dict,
@@ -139,23 +177,8 @@ class GithubCopilotResponsesAPIConfig(OpenAIResponsesAPIConfig):
             # Merge with existing headers (user's extra_headers take priority)
             merged_headers = {**default_headers, **headers}
 
-            # Analyze input to determine additional headers
-            input_param = self._get_input_from_params(litellm_params)
-
-            # Add X-Initiator header based on input analysis
-            if input_param is not None:
-                initiator = self._get_initiator(input_param)
-                merged_headers["X-Initiator"] = initiator
-                verbose_logger.debug(
-                    f"GitHub Copilot Responses API: Set X-Initiator={initiator}"
-                )
-
-                # Add vision header if input contains images
-                if self._has_vision_input(input_param):
-                    merged_headers["copilot-vision-request"] = "true"
-                    verbose_logger.debug(
-                        "GitHub Copilot Responses API: Enabled vision request"
-                    )
+            # X-Initiator and vision headers are set in transform_responses_api_request
+            # where we have access to the input parameter
 
             verbose_logger.debug(
                 f"GitHub Copilot Responses API: Successfully configured headers for model {model}"
@@ -232,26 +255,6 @@ class GithubCopilotResponsesAPIConfig(OpenAIResponsesAPIConfig):
 
     # ==================== Helper Methods ====================
 
-    def _get_input_from_params(
-        self, litellm_params: Optional[GenericLiteLLMParams]
-    ) -> Optional[Union[str, ResponseInputParam]]:
-        """
-        Extract input parameter from litellm_params.
-
-        The input parameter contains the conversation history and is needed
-        for vision detection and initiator determination.
-        """
-        if litellm_params is None:
-            return None
-
-        # Try to get input from litellm_params
-        # This might be in different locations depending on how LiteLLM structures it
-        if hasattr(litellm_params, "input"):
-            return litellm_params.input
-
-        # If not found, return None and let the API handle it
-        return None
-
     def _get_initiator(self, input_param: Union[str, ResponseInputParam]) -> str:
         """
         Determine X-Initiator header value based on input analysis.