### 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_
if isinstance(self.auth_info, dict):
            if self.auth_info.get("identity") is None:
                self.auth_info["identity"] = {}
            return self.auth_info["identity"]
    def is_websocket_request(self):
        upgrade_header = str(self.headers.get("upgrade") or "")
        return upgrade_header.lower() == "websocket"
    def is_v1(self):
        """Whether this is an API Gateway v1 request"""
        return self.apigw_version == ApiGatewayVersion.V1
class ProxyListenerApiGateway(ProxyListener):
    def forward_request(self, method, path, data, headers):
        invocation_context = ApiInvocationContext(method, path, data, headers)
        forwarded_for = headers.get(HEADER_LOCALSTACK_EDGE_URL, "")
        if re.match(PATH_REGEX_USER_REQUEST, path) or "execute-api" in forwarded_for:
            result = invoke_rest_api_from_request(invocation_context)
            if result is not None:
                return result
        data = data and json.loads(to_str(data))
        if re.match(PATH_REGEX_AUTHORIZERS, path):
            return handle_authorizers(method, path, data, headers)
        if re.match(PATH_REGEX_DOC_PARTS, path):
            return handle_documentation_parts(method, path, data, headers)
        if re.match(PATH_REGEX_VALIDATORS, path):
            return handle_validators(method, path, data, headers)
        if re.match(PATH_REGEX_RESPONSES, path):
            return handle_gateway_responses(method, path, data, headers)
        if re.match(PATH_REGEX_PATH_MAPPINGS, path):