fix(eks): incorrect nodegroupName(under feature flag)

[pahud]

Issue # (if applicable)

As #22910 and #25278 were closed for staleness. I am opening a new PR to fix #22442.

To avoid breaking change, this PR introduces a new feature flag for the bug fix.

Closes #22442

The Code for verification

import {
  App, Stack,
  aws_eks as eks,
  aws_ec2 as ec2,
  CfnOutput, cx_api,
} from 'aws-cdk-lib';

const app = new App();
const env = { region: process.env.CDK_DEFAULT_REGION, account: process.env.CDK_DEFAULT_ACCOUNT };
const stack = new Stack(app, 'my-test-stack2', { env });

stack.node.setContext(cx_api.EKS_NODEGROUP_NAME, true);

const vpc = ec2.Vpc.fromLookup(stack, 'Vpc', { isDefault: true });

const cluster = new eks.Cluster(stack, 'Cluster', {
  vpc,
  version: eks.KubernetesVersion.V1_29,
  defaultCapacity: 0,
});

const ng1 = new eks.Nodegroup(stack, 'ng-1', {
  cluster,
});

const ng2 = cluster.addNodegroupCapacity('ng-2', {
  nodegroupName: 'custom-name',
});

new CfnOutput(stack, 'ng1-name', { value: ng1.nodegroupName });
new CfnOutput(stack, 'ng2-name', { value: ng2.nodegroupName });

The output is like

Outputs:
my-test-stack2.ng1name = ng19F1EA947-sSziNMzPVkik
my-test-stack2.ng2name = custom-name

Console:

Checklist

• My code adheres to the CONTRIBUTING GUIDE and DESIGN GUIDELINES

---

By submitting this pull request, I confirm that my contribution is made under the terms of the Apache-2.0 license

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[GavinZZ]

LGTM

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Thank you for contributing! Your pull request will be updated from main and then merged automatically (do not update manually, and be sure to allow changes to be pushed to your fork).

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[mergify]

update

☑️ Nothing to do

• queue-position=-1 [📌 update requirement]
• #commits-behind>0 [📌 update requirement]
• -closed [📌 update requirement]
• -conflict [📌 update requirement]

[TheRealAmazonKendra]

update

☑️ Nothing to do

That's... not true.

[GavinZZ]

@mergify update

[mergify]

update

✅ Branch has been successfully updated

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AWS CodeBuild CI Report

• CodeBuild project: AutoBuildv2Project1C6BFA3F-wQm2hXv2jqQv
• Commit ID: 32a0090
• Result: SUCCEEDED
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