### Is there an existing issue for this?

- [X] I have searched the existing issues and read the documentation

### Question

Using a websocket apigatewayv2 in localstack and i need to change the body of the request e.g. add the connectionid, which is something i can do with a HTTP integration on the AWS gateway, however when I try this with localstack i receive the following error "Unsupported integration type "HTTP" for Websocket API ID" and then prints the ID of the API, if this feature is not enabled then how should we test the actual API where the connectionId and other things are added to the request body

### Anything else?

_No response_
response.multi_value_headers = parsed_result.get("multiValueHeaders") or {}
            
            response._content = apply_template(integration, "response", response._content)
            response.headers["Content-Length"] = str(len(response.content or ""))
            return response
        raise Exception(
            'API Gateway integration type "%s", action "%s", method "%s" invalid or not yet implemented'
            % (integration_type, uri, method)
        )
    elif integration_type == "AWS":
        if "kinesis:action/" in uri:
            if uri.endswith("kinesis:action/PutRecord"):
                target = kinesis_listener.ACTION_PUT_RECORD
            elif uri.endswith("kinesis:action/PutRecords"):
                target = kinesis_listener.ACTION_PUT_RECORDS
            elif uri.endswith("kinesis:action/ListStreams"):
                target = kinesis_listener.ACTION_LIST_STREAMS
            else:
                LOG.info(
                    "Unexpected API Gateway integration URI '%s' for integration type %s",
                    uri,
                    integration_type,
                )
                target = ""
            
            new_data = apply_request_response_templates(
                data, integration.get("requestTemplates"), content_type=APPLICATION_JSON
            )
            
            headers = aws_stack.mock_aws_request_headers(service="kinesis")