fix(slack): use root logger for 500 error alerts

Exception handler used named logger which may not propagate to
root logger's SlackHandler. Use logging.getLogger() (root) directly
to guarantee Slack notifications for unhandled exceptions.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: ImTotem

src/bcsd_api/exception/handlers.py

@@ -5,7 +5,7 @@
 
 from .base import AppException
 
-logger = logging.getLogger(__name__)
+logger = logging.getLogger("bcsd_api.error")
 
 
 def register_handlers(app: FastAPI) -> None:
@@ -16,6 +16,8 @@ async def _handle(request: Request, exc: AppException) -> JSONResponse:
 
     @app.exception_handler(Exception)
     async def _unhandled(request: Request, exc: Exception) -> JSONResponse:
-        logger.error("%s %s: %s", request.method, request.url.path, exc, exc_info=exc)
+        logging.getLogger().error(
+            "%s %s: %s", request.method, request.url.path, exc, exc_info=exc,
+        )
         body = {"error_code": "INTERNAL_ERROR", "message": "internal server error"}
         return JSONResponse(status_code=500, content=body)