AWS WebSocket and Lambda Authorizer issue

I am trying AWS WebSocket API and Lambda authorizer, I configured the authorizer for the connect route already which is triggered for connect too. However, in AWS console for the Lambda authorizer, I saw this error in its trigger(API Gateway) config: "The API with ID 7rypk365yl doesn’t include a route with path /* having an integration arn:aws:lambda:us-east-1:370783930566:function:apigwLambdaAuthorizer."

For WebSocket API, I only need config the Lambda authorizer for the connect route? Above error feel like applies to REST/HTTP API only? Have I mixed up API Gateway v1 and v2 in some way? I did refer to some examples for REST/HTTP or the WebSocket document refers to REST one for common part.

Thanks in advance!