feat: add OpenAI /v1/responses adapter via chat flow

Implement a thin responses layer that reuses existing chat/completions execution so auth, pooling, streaming, tool passthrough, and error semantics stay aligned across APIs.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

app/openai_schema.py

@@ -32,6 +32,19 @@ class ChatCompletionsRequest(BaseModel):
     tool_choice: Any | None = None
 
 
+class ResponsesRequest(BaseModel):
+    model: str
+    input: Any | None = None
+    stream: bool = False
+    temperature: float | None = None
+    top_p: float | None = None
+    max_output_tokens: int | None = None
+    user: str | None = None
+    tools: list[dict[str, Any]] | None = None
+    tool_choice: Any | None = None
+    instructions: str | None = None
+
+
 class ModelData(BaseModel):
     id: str
     name: str | None = None