How to allign the Name Servers of Route53 Public Hosted Zone and Registered Domains in CDK?

In my account is an "registered domain" with 4 nameservers assigned to it. To originally created Public Hosted Zone was deleted as I want it to be created with the CDK deployment.

When deploying the Route53 Public Hosted Zone it is each time creating a new set of Name Servers. Solution s then to update the Name Servers of the registered domain manually. This issue is described in the following link as well together with an manual fix: https://docs.aws.amazon.com/Route53/latest/DeveloperGuide/domain-replace-hosted-zone.html

Problem: I don't want to change the Name Servers manually, but directly with CDK.

• I didnt see any possibility in the Constructor to set the Hosted Zones when deploying https://docs.aws.amazon.com/cdk/api/v2/docs/aws-cdk-lib.aws_route53.PublicHostedZone.html
• Neither i saw how to change the name servers of the registered domain automatically via CDK
• When creating a ZoneDelegationRecord (see code in the following) i could add the target Name Servers but it fails during build

Question: How to create a Public Hosted Zone and link it to a registered Domain with both sharing the same Name Servers via CDK?

Code:

import * as route53 from 'aws-cdk-lib/aws-route53';
import { RemovalPolicy, Tags, Duration } from 'aws-cdk-lib';


const route53PublicHostedZone = new route53.PublicHostedZone(scope, 'route53PublicHostedZone', {
    zoneName: 'myWhatEverDomain.com',
  });

const zoneDelegationRecord = new route53.ZoneDelegationRecord(scope, 'MyZoneDelegationRecord', {
    // real NS Names are different of course
    nameServers: [
      'ns-1.awsdns-1.org',
      'ns-2.awsdns-2.net',
      'ns-3.awsdns-3.co.uk',
      'ns-4.awsdns-4.com'],
    zone: route53PublicHostedZone,
    ttl: Duration.minutes(1),
  });

Error:

Failed resources:
myCdkStack | 16:53:12 | CREATE_FAILED        | AWS::Route53::RecordSet                   | MyZoneDelegationRecord (MyZoneDelegationRecordD1ECAA29) [Tried to create resource record set [name='myWhatEverDomain.com.', type='NS'] but it already exists]

 myCdkStack  failed: Error: The stack named myCdkStack failed creation, it may need to be manually deleted from the AWS console: ROLLBACK_COMPLETE
    at Object.waitForStackDeploy (C:\Users\myUser\AppData\Roaming\npm\node_modules\aws-cdk\lib\api\util\cloudformation.ts:307:11)
    at processTicksAndRejections (node:internal/process/task_queues:96:5)
    at prepareAndExecuteChangeSet (C:\Users\myUser\AppData\Roaming\npm\node_modules\aws-cdk\lib\api\deploy-stack.ts:355:26)
    at CdkToolkit.deploy (C:\Users\myUser\AppData\Roaming\npm\node_modules\aws-cdk\lib\cdk-toolkit.ts:201:24)
    at initCommandLine (C:\Users\myUser\AppData\Roaming\npm\node_modules\aws-cdk\bin\cdk.ts:281:9)

The stack named pmyCdkStack failed creation, it may need to be manually deleted from the AWS console: ROLLBACK_COMPLETE