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*

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) {

packages/@aws-cdk-testing/framework-integ/test/aws-eks/test/integ.eks-al2023-nodegroup.js.snapshot/aws-cdk-eks-cluster-al2023-nodegroup-test.template.json

@@ -434,9 +434,9 @@
      "S3Bucket": {
       "Fn::Sub": "cdk-hnb659fds-assets-${AWS::AccountId}-${AWS::Region}"
      },
-     "S3Key": "bfbdea4d45250c8162c204fe0687cb775e24d61c895ad89e4ca6e9a7fc90b0f0.zip"
+     "S3Key": "f3c812b299b0759c937b41e39d3451f5cc61279c2ec9ee791fac08ba1e56508b.zip"
     },
-    "Description": "/opt/kubectl/kubectl 1.30; /opt/helm/helm 3.15",
+    "Description": "/opt/kubectl/kubectl 1.31.0; /opt/helm/helm 3.16.1",
     "LicenseInfo": "Apache-2.0"
    }
   },
@@ -755,7 +755,7 @@
      ]
     },
     "Config": {
-     "version": "1.30",
+     "version": "1.31",
      "roleArn": {
       "Fn::GetAtt": [
        "ClusterRoleFA261979",
@@ -1091,7 +1091,7 @@
        {
         "Fn::Sub": "cdk-hnb659fds-assets-${AWS::AccountId}-${AWS::Region}"
        },
-       "/7e3a4db62580d1e348e643295ab4a2ae196cf491b19e8bb2af0e5df5731f8c44.json"
+       "/b59c66f745e83613dbb82872f6a80f1836e60dc270d4a996addaec59b6c48723.json"
       ]
      ]
     }
@@ -1141,7 +1141,7 @@
        {
         "Fn::Sub": "cdk-hnb659fds-assets-${AWS::AccountId}-${AWS::Region}"
        },
-       "/9bf54635ece475c4a80e427fbac6f464603ed4d3db0993521bf2ed14fe8f2fcb.json"
+       "/79cbaf26aa922a95f542628df5997344482c9da45613b7f2df0c0702cf0aa1d2.json"
       ]
      ]
     }

packages/@aws-cdk-testing/framework-integ/test/aws-eks/test/integ.eks-al2023-nodegroup.js.snapshot/awscdkeksclusteral2023nodegrouptestawscdkawseksClusterResourceProviderE67D0702.nested.template.json

@@ -7,7 +7,7 @@
      "S3Bucket": {
       "Fn::Sub": "cdk-hnb659fds-assets-${AWS::AccountId}-${AWS::Region}"
      },
-     "S3Key": "22de69e75b55e15d4d49905d8a4901edd66d1367f617c2a01ac6e86ca2b7eb84.zip"
+     "S3Key": "93d96d34e0d3cd20eb082652b91012b131bdc34fcf2bc16eb4170e04772fddb1.zip"
     },
     "Description": "/opt/nodejs/node_modules/proxy-agent"
    }
@@ -50,7 +50,7 @@
      "S3Bucket": {
       "Fn::Sub": "cdk-hnb659fds-assets-${AWS::AccountId}-${AWS::Region}"
      },
-     "S3Key": "1eaf141d4012ab0977a33bdf864ebbc6aa869a607e97fab6cd231fe6ef503aec.zip"
+     "S3Key": "9f065b22983c18e9b152e9fcfadacd16e29faaee10e05efe72c920ee3de01d63.zip"
     },
     "Description": "onEvent handler for EKS cluster resource provider",
     "Environment": {
@@ -123,7 +123,7 @@
      "S3Bucket": {
       "Fn::Sub": "cdk-hnb659fds-assets-${AWS::AccountId}-${AWS::Region}"
      },
-     "S3Key": "1eaf141d4012ab0977a33bdf864ebbc6aa869a607e97fab6cd231fe6ef503aec.zip"
+     "S3Key": "9f065b22983c18e9b152e9fcfadacd16e29faaee10e05efe72c920ee3de01d63.zip"
     },
     "Description": "isComplete handler for EKS cluster resource provider",
     "Environment": {
@@ -265,7 +265,7 @@
      "S3Bucket": {
       "Fn::Sub": "cdk-hnb659fds-assets-${AWS::AccountId}-${AWS::Region}"
      },
-     "S3Key": "46fb886516825167db3571f1ed91110fc6163ce20ee26fdb097c2c983f25fcd6.zip"
+     "S3Key": "d320874294f5d626406d5f86087c2a2c8e6efc0aab690c5105572555dc445fd4.zip"
     },
     "Description": "AWS CDK resource provider framework - onEvent (aws-cdk-eks-cluster-al2023-nodegroup-test/@aws-cdk--aws-eks.ClusterResourceProvider/Provider)",
     "Environment": {
@@ -410,7 +410,7 @@
      "S3Bucket": {
       "Fn::Sub": "cdk-hnb659fds-assets-${AWS::AccountId}-${AWS::Region}"
      },
-     "S3Key": "46fb886516825167db3571f1ed91110fc6163ce20ee26fdb097c2c983f25fcd6.zip"
+     "S3Key": "d320874294f5d626406d5f86087c2a2c8e6efc0aab690c5105572555dc445fd4.zip"
     },
     "Description": "AWS CDK resource provider framework - isComplete (aws-cdk-eks-cluster-al2023-nodegroup-test/@aws-cdk--aws-eks.ClusterResourceProvider/Provider)",
     "Environment": {
@@ -552,7 +552,7 @@
      "S3Bucket": {
       "Fn::Sub": "cdk-hnb659fds-assets-${AWS::AccountId}-${AWS::Region}"
      },
-     "S3Key": "46fb886516825167db3571f1ed91110fc6163ce20ee26fdb097c2c983f25fcd6.zip"
+     "S3Key": "d320874294f5d626406d5f86087c2a2c8e6efc0aab690c5105572555dc445fd4.zip"
     },
     "Description": "AWS CDK resource provider framework - onTimeout (aws-cdk-eks-cluster-al2023-nodegroup-test/@aws-cdk--aws-eks.ClusterResourceProvider/Provider)",
     "Environment": {

packages/@aws-cdk-testing/framework-integ/test/aws-eks/test/integ.eks-al2023-nodegroup.js.snapshot/awscdkeksclusteral2023nodegrouptestawscdkawseksKubectlProvider3D3ED876.nested.template.json

@@ -7,7 +7,7 @@
      "S3Bucket": {
       "Fn::Sub": "cdk-hnb659fds-assets-${AWS::AccountId}-${AWS::Region}"
      },
-     "S3Key": "abc70c90ded969d12235ca11768293cb20557cff54518518480c0d9fb344a098.zip"
+     "S3Key": "024d0b8c5d7cf69ece484efe22f1647e273f484175ef3b79df543b7538da9c81.zip"
     },
     "Description": "onEvent handler for EKS kubectl resource provider",
     "Environment": {
@@ -151,7 +151,7 @@
      "S3Bucket": {
       "Fn::Sub": "cdk-hnb659fds-assets-${AWS::AccountId}-${AWS::Region}"
      },
-     "S3Key": "46fb886516825167db3571f1ed91110fc6163ce20ee26fdb097c2c983f25fcd6.zip"
+     "S3Key": "d320874294f5d626406d5f86087c2a2c8e6efc0aab690c5105572555dc445fd4.zip"
     },
     "Description": "AWS CDK resource provider framework - onEvent (aws-cdk-eks-cluster-al2023-nodegroup-test/@aws-cdk--aws-eks.KubectlProvider/Provider)",
     "Environment": {