[Python] How to make a custom error message for Service Unavailable in FastAPI?

I'm running my app like so:

uvicorn main:app --host 0.0.0.0 --port 8080 --workers 2 --limit-concurrency 10


Versions are:

fastapi==0.103.2
uvicorn==0.34.3


When I start slamming it, I get the expected 503 Service Unavailable error.

I want to have a custom error message when this happens.

I thought this code would catch this error, but that code never gets touched when I get a 503.

What am I doing wrong?

app = FastAPI()


class ServiceUnavailableException(Exception):
def __init__(self, message: str):
self.message = message


@app.exception_handler(ServiceUnavailableException)
async def service_unavailable_exception_handler(request: Request, exc: ServiceUnavailableException):
return JSONResponse(
status_code=status.HTTP_503_SERVICE_UNAVAILABLE, # Use 503 status code
content={"message": exc.message}
)

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