[EKS] [request]: add "cluster name" to metadata endpoint

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**Tell us about your request**
What do you want us to build?
A metadata endpoint for EKS clusters that allow applications running within the cluster to get information about a cluster without querying an AWS API. The downward API only provides information about the pod.

**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?**
What outcome are you trying to achieve, ultimately, and why is it hard/impossible to do right now? What is the impact of not having this problem solved? The more details you can provide, the better we'll be able to understand and solve the problem.
I am trying to get the name of the cluster that a pod in running on from within the pod itself.

**Are you currently working around this issue?**
How are you currently solving this problem?
I am still debating how to tackle this.

**Additional context**
Anything else we should know?

**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.)

The issue describes an EKS metadata endpoint for applications running inside a cluster; no repository files, tests, or entry points are identified. Start by reviewing the project’s EKS roadmap context and determine the endpoint’s intended access and response behavior. Done means applications can obtain the cluster name without querying an AWS API.

Written by the indexing model from the issue text.