fix(mypy): widen file-ref helper input type, annotate empty list

- _resolve_file_references / _async_resolve_file_references: param type
  EmbeddingInput → Union[EmbeddingInput, List[str]]. Two of the four
  call sites pass flat_elements (List[str]) post-410f54dc72; the
  function body already handles both shapes at runtime — only the type
  was lying.
- transform_openai_input_gemini_content: annotate text_elements as
  List[str] for the var-annotated rule.

litellm/llms/vertex_ai/gemini_embeddings/batch_embed_content_handler.py

@@ -48,7 +48,7 @@ class GoogleBatchEmbeddings(VertexLLM):
 
     def _resolve_file_references(
         self,
-        input: EmbeddingInput,
+        input: Union[EmbeddingInput, List[str]],
         api_key: str,
         sync_handler: HTTPHandler,
     ) -> Dict[str, Dict[str, str]]:
@@ -87,7 +87,7 @@ class GoogleBatchEmbeddings(VertexLLM):
 
     async def _async_resolve_file_references(
         self,
-        input: EmbeddingInput,
+        input: Union[EmbeddingInput, List[str]],
         api_key: str,
         async_handler: AsyncHTTPHandler,
     ) -> Dict[str, Dict[str, str]]:

litellm/llms/vertex_ai/gemini_embeddings/batch_embed_content_transformation.py

@@ -361,7 +361,7 @@ def process_response(
     has_nested = isinstance(input, list) and any(isinstance(e, list) for e in input)
     if _is_multimodal_input(input) or has_nested:
         input_list = input if isinstance(input, list) else [input]
-        text_elements = []
+        text_elements: List[str] = []
         for e in input_list:
             if isinstance(e, list):
                 text_elements.extend(