[EKS] [request]: Support for Kubernetes 1.37

### Community Note

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**Tell us about your request**
https://kubernetes.io/blog/2026/08/26/kubernetes-v1-37-release/

I'd like to be able to use Kubernetes 1.37 on EKS and be aware of the release timeline to help plan for it. This issue was opened to track progress on the new release.

**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?**
n/a

**Are you currently working around this issue?**
n/a

**Additional context**
n/a

**Attachments**
If you think you might have additional information that you'd like to include via an attachment, please do - we'll take a look. (Remember to remove any personally-identifiable information.)

No repository files, tests, or code entry points are identified in the issue. Start with the linked Kubernetes 1.37 release information and the EKS service context; done would require tracking or delivering EKS support and documenting the release timeline.

Written by the indexing model from the issue text.