[EKS] [request]: Support for changing the EKS cluster role

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**Tell us about your request**
Support for changing the EKS cluster role (the roleArn used during CreateCluster operation) - https://docs.aws.amazon.com/eks/latest/userguide/cluster-iam-role.html

**Which service(s) is this request for?**
EKS

**Tell us about the problem you're trying to solve. What are you trying to do, and why is it hard?**
We have a couple of clusters using the same IAM cluster role, and we would like to change it (having separate roles per cluster to independently control their lifecycle via Terraform).

**Are you currently working around this issue?**
There is no workaround apart from redeploying the EKS cluster.

**Additional context**
This was also reported to support as case 174834701700704 in May 2025 with the following response:

> Hello.
> Thank you for contacting AWS Premium Support. My name is Yeorae and I have taken ownership of this case.
> From your correspondence, I understand that you are looking for a way to change the cluster IAM role after the cluster creation. Please let me know if I misunderstand your concern.
>
> Based on the internal investigation, modification of the cluster's role after creation is not currently supported.
> If you need to change the Cluster IAM role associated with an EKS cluster, you would need to create a new EKS cluster with the desired IAM role configuration and currently this way is the only option.
> Please note that migrating workloads and configurations from the old cluster to the new one can be a complex process and may involve recreating resources such as worker nodes, pods, and services in the new cluster.
>
> I checked that there is an internal feature request for the functionality to change/modify cluster roles after cluster creation, and added a comment for the request on your behalf to indicate your interest in this feature.
> However, please note that as of now, I will not be able to provide an ETA for the feature to be released, but rest assured that this will be looked at for feasibility by the Product team.
>
> I sincerely hope that you find the above information useful.
> Please feel free to bring any further concerns or information to me and I'll be glad to assist.
> Have a safe and good day ahead.

**Attachments**
N/A

This is an AWS EKS product request rather than a repository implementation task; no files or tests are identified. Start by reviewing the EKS cluster IAM role behavior and the linked AWS documentation. Done would require AWS support for changing the roleArn after cluster creation without redeploying the cluster.

Written by the indexing model from the issue text.