fix(eks): albController incompatibility with AuthenticationMode.API m…

…ode (#31258)

### Issue # (if applicable)

This PR improve the compatibility for `albController` with `authenticationMode.API`

related to #30888

We will address Fargate compatibility in #31267

### Reason for this change

- When `authenticationMode.API` is specified, no aws-auth configMap should be created
- albController should not depend on `cluster.awsAuth` because that would create aws-auth configmap, which is not required in `API` mode.



### Description of changes



### Description of how you validated changes

**unit tests**
- validate the behavior in all conditions of the `authenticationMode`

**integ test**
- add a new integ test with API mode to ensure successful deployment


## debugger

```js
{
  "version": "0.2.0",
  "configurations": [
    {
      "type": "node",
      "request": "launch",
      "name": "Jest",
      "program": "${workspaceFolder}/node_modules/jest/bin/jest.js",
      "cwd": "${workspaceFolder}/packages/aws-cdk-lib",
      "args": [
        "--verbose",
        "-i",
        "--no-cache",
        "test/alb-controller.test.ts",
      ],
      "console": "integratedTerminal",
      "internalConsoleOptions": "neverOpen",
      "skipFiles": [
        "<node_internals>/**"
      ],
      "outFiles": [
        "${workspaceFolder}/**/*.(m|c|)js",
        "!**/node_modules/**"
      ],
    }
  ]
}
```



### 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*