fix(eks): cluster deployment issue when the authentication mode is not changing (#33680)

### Reason for this change

The issue happens in a very small edge case:
1. create a eks.Cluster like this
```
new eks.Cluster(this, 'Cluster', {
    version: eks.KubernetesVersion.V1_32,
    kubectlLayer: new KubectlV32Layer(this, 'KubectlLayer'),
});
```
2. In EKS console, modify the Auth model from CONFIG_MAP to API_AND_CONFIG_MAP, wait a few minutes until it completes.

3. Again, update from API_AND_CONFIG_MAP to API from console, wait until it completes

4. Now in CDK, add
```
authenticationMode: eks.AuthenticationMode.API,
```
5. When we re-deploy, CDK would have a validation error:
```
Received response status [FAILED] from custom resource. Message returned: Cannot update from undefined(CONFIG_MAP) to API
```
It is because in local template, the auth mode is `Config_Map` while the actual resource is using `API` mode. In this case, cdk deployment should ignore the update instead of throwing an error.

### Description of changes

Move the code order a little bit. Basically check if the updated auth mode is the same as existing mode first then do some validations.






### Description of how you validated changes

Existing unit tests/integration tests passed. I removed 2 unit tests which are not applicable because `DescribeCluster` api call will always return auth mode.

Manually tested the change in the edge case. 

### Checklist
- [ ] 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: xazhao

packages/@aws-cdk/custom-resource-handlers/lib/aws-eks/cluster-resource-handler/cluster.ts

@@ -218,6 +218,18 @@ export class ClusterResourceHandler extends ResourceHandler {
       }
 
       if (updates.updateAuthMode) {
+        // update-authmode will fail if we try to update to the same mode,
+        // so skip in this case.
+        try {
+          const cluster = (await this.eks.describeCluster({ name: this.clusterName })).cluster;
+          if (cluster?.accessConfig?.authenticationMode === this.newProps.accessConfig?.authenticationMode) {
+            console.log(`cluster already at ${cluster?.accessConfig?.authenticationMode}, skipping authMode update`);
+            return;
+          }
+        } catch (e: any) {
+          throw e;
+        }
+
         // the update path must be
         // `undefined or CONFIG_MAP` -> `API_AND_CONFIG_MAP` -> `API`
         // and it's one way path.
@@ -247,17 +259,6 @@ export class ClusterResourceHandler extends ResourceHandler {
           this.newProps.accessConfig?.authenticationMode === 'API') {
           throw new Error('Cannot update from CONFIG_MAP to API');
         }
-        // update-authmode will fail if we try to update to the same mode,
-        // so skip in this case.
-        try {
-          const cluster = (await this.eks.describeCluster({ name: this.clusterName })).cluster;
-          if (cluster?.accessConfig?.authenticationMode === this.newProps.accessConfig?.authenticationMode) {
-            console.log(`cluster already at ${cluster?.accessConfig?.authenticationMode}, skipping authMode update`);
-            return;
-          }
-        } catch (e: any) {
-          throw e;
-        }
         config.accessConfig = this.newProps.accessConfig;
       }
 

packages/@aws-cdk/custom-resource-handlers/test/aws-eks/cluster-resource-handler-mocks.ts

@@ -90,6 +90,7 @@ export const client: EksClient = {
         arn: 'arn:cluster-arn',
         certificateAuthority: { data: 'certificateAuthority-data' },
         endpoint: 'http://endpoint',
+        accessConfig: { authenticationMode: 'CONFIG_MAP' },
         status: simulateResponse.describeClusterResponseMockStatus || 'ACTIVE',
       },
     };

packages/@aws-cdk/custom-resource-handlers/test/aws-eks/cluster-resource-provider.test.ts

@@ -590,21 +590,6 @@ describe('cluster resource provider', () => {
 
           expect(error.message).toEqual('Cannot fallback authenticationMode from defined to undefined');
         });
-        test('fails from API_AND_CONFIG_MAP to CONFIG_MAP', async () => {
-          const handler = new ClusterResourceHandler(mocks.client, mocks.newRequest('Update', {
-            accessConfig: { authenticationMode: 'CONFIG_MAP' },
-          }, {
-            accessConfig: { authenticationMode: 'API_AND_CONFIG_MAP' },
-          }));
-          let error: any;
-          try {
-            await handler.onEvent();
-          } catch (e) {
-            error = e;
-          }
-
-          expect(error.message).toEqual('Cannot fallback authenticationMode from API_AND_CONFIG_MAP to CONFIG_MAP');
-        });
         test('fails from API to undefined', async () => {
           const handler = new ClusterResourceHandler(mocks.client, mocks.newRequest('Update', {
             accessConfig: { authenticationMode: undefined },
@@ -635,21 +620,6 @@ describe('cluster resource provider', () => {
 
           expect(error.message).toEqual('Cannot fallback authenticationMode from API to API_AND_CONFIG_MAP');
         });
-        test('fails from API to CONFIG_MAP', async () => {
-          const handler = new ClusterResourceHandler(mocks.client, mocks.newRequest('Update', {
-            accessConfig: { authenticationMode: 'CONFIG_MAP' },
-          }, {
-            accessConfig: { authenticationMode: 'API' },
-          }));
-          let error: any;
-          try {
-            await handler.onEvent();
-          } catch (e) {
-            error = e;
-          }
-
-          expect(error.message).toEqual('Cannot fallback authenticationMode from API to CONFIG_MAP');
-        });
         test('fails from undefined to API', async () => {
           const handler = new ClusterResourceHandler(mocks.client, mocks.newRequest('Update', {
             accessConfig: { authenticationMode: 'API' },