The metrics-server-v0.3.6 deployment that is installed into GKE clusters by default is using an outdated version of addon-resizer (addon-resizer:1.8.11-gke.0) that causes CPU utilization and throttling issues. See here
The cluster running is on the latest version of the regular release branch (1.20.8-gke.900), when editing the metric-server workload deployment and changing the version of addon-resizer to addon-resizer-1.8.14 the deployment reverts back to the old version that is managed by google.
Is there a way to change the image that the metrics-server-nanny container deployment is using permanently or is there a way to update the entire metrics-server deployment so that the containers that are running are on an update version?
You cannot update those deployments. Any updates you make will be reverted to the original deployment spec.
Looks like the "fix" will be released with 1.22 and initially backported to 1.21 as well. It will likely make it back to 1.19+ eventually.