Unable to Upgrade EKS Control Plane or Managed Node Groups

You should follow this guide https://docs.aws.amazon.com/eks/latest/userguide/kubernetes-versions.html to make sure you keep your cluster upgraded before it is in end of support. If you are using gitops (with argocd or flux), you can create a new cluster and sync your yaml's from git to the new cluster. If you are not using gitops you can create a snapshot of all the yamls in your cluster with a tool like https://velero.io/ and recreate your resources in a new cluster from the snapshot yamls's

For future reference, you can create a self managed node group with the desired version for the nodes and then upgrade the cluster version.

I used eksctl to create the self managed node groups but found it would update the existing security group rules and that it would also affect the aws-load-balancer-controller because of the newly created security groups. There was a bit of downtime for the time it took to manually update the security groups and the load balancer target groups.