I am having trouble setting up a WebSocket API Gateway that calls a Lambda function.

These docs say:

Important

For proxy integrations, API Gateway automatically passes the backend output to the caller as the complete payload. There is no integration response.

However, with the following lambda code:

def lambda_handler(event, context):
    return {"example": "response"}

I am getting the following error in CloudWatch logs: "Execution failed due to configuration error: Malformed Lambda proxy response"

I tried returning it as a string, which didn't work. Eventually I got something that didn't give an error:

def lambda_handler(event, context):
    return {"statusCode": 200}

Which returned an empty message to the client, and no error in CloudWatch. I tried changing the status code to 404, and it didn't make a difference (still worked), but I set it to None and that gave an error in CloudWatch again.

This makes very little sense to me because:

1. WebSocket messages don't have status codes, that's an HTTP thing.
2. The docs specifically say that the output is passed directly through to the caller, so I don't understand why this error is even happening at all.

Does anyone have any insight on what is going on here and the proper way to set this up? Thanks.