restructure: move backend into backend/

backend/app/errors.py

@@ -0,0 +1,15 @@
+from fastapi import Request
+from fastapi.responses import JSONResponse
+
+
+class APIError(Exception):
+    """Application error that maps to a JSON response with a status code."""
+
+    def __init__(self, status_code: int, detail: str):
+        self.status_code = status_code
+        self.detail = detail
+        super().__init__(detail)
+
+
+async def api_error_handler(request: Request, exc: APIError) -> JSONResponse:
+    return JSONResponse(status_code=exc.status_code, content={"detail": exc.detail})