feat(eks): support eks with k8s 1.31 (#31707)

### Issue # (if applicable)

Closes #31695

### Reason for this change

- Similar to #30454, this PR adds 1.31 support.
- Update all existing integ tests for V1_30 and make sure they deploy with V1_31.


### Description of changes



### Description of how you validated changes


```ts
import * as ec2 from 'aws-cdk-lib/aws-ec2';
import * as iam from 'aws-cdk-lib/aws-iam';
import { App, Stack, StackProps } from 'aws-cdk-lib';
import { KubectlV31Layer } from '@aws-cdk/lambda-layer-kubectl-v31';
import * as eks from 'aws-cdk-lib/aws-eks';
import { Construct } from 'constructs';

export class EksClusterLatestVersion extends Stack {
  constructor(scope: Construct, id: string, props: StackProps) {
    super(scope, id, props);

    const vpc = new ec2.Vpc(this, 'Vpc', { natGateways: 1 });
    const mastersRole = new iam.Role(this, 'Role', {
      assumedBy: new iam.AccountRootPrincipal(),
    });

    new eks.Cluster(this, 'Cluster', {
      vpc,
      mastersRole,
      version: eks.KubernetesVersion.V1_31,
      kubectlLayer: new KubectlV31Layer(this, 'KubectlLayer'),
      defaultCapacity: 1,
    });
  }
}

const app = new App();
new EksClusterLatestVersion(app, 'v31-stack', {
  env: {
    account: process.env.CDK_DEFAULT_ACCOUNT,
    region: process.env.CDK_DEFAULT_REGION,
  },
})
```

verify

```sh
$ kubectl get no
NAME                           STATUS   ROLES    AGE     VERSION
ip-10-0-183-173.ec2.internal   Ready    <none>   4m25s   v1.31.0-eks-a737599
```

### Checklist
- [x] My code adheres to the [CONTRIBUTING GUIDE](https://github.com/aws/aws-cdk/blob/main/CONTRIBUTING.md) and [DESIGN GUIDELINES](https://github.com/aws/aws-cdk/blob/main/docs/DESIGN_GUIDELINES.md)

----

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

Author: pahud

packages/@aws-cdk-testing/framework-integ/package.json

@@ -42,6 +42,7 @@
     "@aws-cdk/lambda-layer-kubectl-v24": "^2.0.242",
     "@aws-cdk/lambda-layer-kubectl-v29": "^2.1.0",
     "@aws-cdk/lambda-layer-kubectl-v30": "^2.0.1",
+    "@aws-cdk/lambda-layer-kubectl-v31": "^2.0.0",
     "aws-cdk-lib": "0.0.0",
     "cdk8s": "2.69.0",
     "cdk8s-plus-27": "2.9.5",

packages/@aws-cdk-testing/framework-integ/test/aws-eks/test/integ-tests-kubernetes-version.ts

@@ -2,6 +2,7 @@ import * as lambda from 'aws-cdk-lib/aws-lambda';
 import { KubectlV24Layer } from '@aws-cdk/lambda-layer-kubectl-v24';
 import { KubectlV29Layer } from '@aws-cdk/lambda-layer-kubectl-v29';
 import { KubectlV30Layer } from '@aws-cdk/lambda-layer-kubectl-v30';
+import { KubectlV31Layer } from '@aws-cdk/lambda-layer-kubectl-v31';
 import { Construct } from 'constructs';
 import * as eks from 'aws-cdk-lib/aws-eks';
 
@@ -13,6 +14,7 @@ const versionMap: { [key: string]: new (scope: Construct, id: string) => lambda.
   '1.24': KubectlV24Layer,
   '1.29': KubectlV29Layer,
   '1.30': KubectlV30Layer,
+  '1.31': KubectlV31Layer,
 };
 
 export function getClusterVersionConfig(scope: Construct, version?: eks.KubernetesVersion) {