Using a HorizontalPodAutoscaler [1] you can scale up and down the amount of "pods" (a grouping of containers that are scheduled as a unit) based on the desired metric.
[1]: https://kubernetes.io/docs/tasks/run-application/horizontal-...
[1]: https://kubernetes.io/docs/tasks/run-application/horizontal-...
Is there some sort of a PID-feedback-loop control that monitors the CPU/memory load and helps spin up more instances if it sees more traffic? If Kubernetes doesn't do that, what piece of software can help automatically scale if there is a huge traffic spike?
Load balance AFAIK doesn't do that. It just helps distribute the load.