How to add containers to a Kubernetes pod on runtime

From this GitHub issue, it seems that the answer is that adding or removing containers to a pod is not possible, since the container list in the pod spec is immutable.

In kubernetes 1.16, there is an alpha feature that would allow for creation of ephemeral containers which could be "added" to running pods. Note, that this requires a feature gate to be enabled on relevant components e.g. kubelet. This may be hard to enable on control plane for cloud provider managed services such as EKS.

API Reference 1.16

Simple tutorial