This question is in context of Pro/Enterprise openvidu licence.
The call recording goes to AWS S3. Our application is on GCloud. Do I need to implement logic to pull and push the recording to GCS or id there any solution already available?
See How other instance of openvidu knows about the session created on another instance of openvidu-server.
If you have deployed OpenVidu in Google Cloud following the On Premises instructions, there is no need to use AWS S3 storage if your recordings are going to be finally stored in GCS. Just implement your own logic to transfer the recordings from the OpenVidu nodes to GCS once they reach ready status (see the description for ready property of the Recording object: REST API - OpenVidu Docs)