AWS WebSocket Lambda Authorizer 403 error

Hi, I am trying AWS WebSocket API with Request Lambda authorizer, the API GW always return 403 or denied though the Lambda authorizer returns allowed result.
Looks like there are 2 versions of the Lambda response format with 2nd version having explicit "isAuthorized".

I am using the default version 1 and haven't checked how to config to user version 2 yet. <br> However, I am expecting version 1 to work too.

Here is an example response from the Lambda authorizer:

{
    "principalId": "*",
    "policyDocument": {
        "Version": "2012-10-17",
        "Statement": [
            {
                "Action": "execute-api:Invoke",
                "Effect": "Allow",
                "Resource": [
                    "arn:aws:execute-api:us-east-1:{account-id-here}:{api-id-here}/development/*/*"
                ]
            }
        ]
    },
    "context": {
        "HeaderAuth1": "cmsn=s001&ts=10162023&signature=abcde12345",
        "isAuthorized": true 
    }
}

I've tried different values for principalId since we don't have one as the TOKEN authorizer case. If I move "isAuthorized" to top level in the response as format v2, API GW says it's unrecognized - guess I need config it to use version 2?

Any clue about possible cause?

Thanks in advance!