`@aws-cdk/aws-pipes-sources-alpha`: adding `deadLetterTarget` results in a failed update

### Describe the bug

I successfully deployed the following Stack:

```ts
const ddbTable = new TableV2(this, "DDBTable", {
tableName: "ddb-table",
partitionKey: {
name: "Location",
type: AttributeType.STRING,
},
dynamoStream: StreamViewType.NEW_AND_OLD_IMAGES,
removalPolicy: RemovalPolicy.DESTROY,
});

const queue = new Queue(this, "Queue", {
retentionPeriod: Duration.days(14),
});

const dlq = new Queue(this, "DLQ", {
retentionPeriod: Duration.days(14),
});

const pipeSource = new DynamoDBSource(ddbTable, {
startingPosition: DynamoDBStartingPosition.LATEST,
batchSize: 1,
maximumRetryAttempts: 0,
// deadLetterTarget: dlq,
});

new Pipe(this, "Pipe", {
source: pipeSource,
target: new SqsTarget(queue),
});
```

### Regression Issue

- [ ] Select this option if this issue appears to be a regression.

### Last Known Working CDK Version

_No response_

### Expected Behavior

Expected `deadLetterTarget` property to work correctly.

### Current Behavior

After uncommenting the `deadLetterTarget` property and deploying again, I get the following error:

```sh
9:12:13 AM | UPDATE_FAILED | AWS::Pipes::Pipe | PipeBFF4E827
Resource handler returned message: "Resource of type 'AWS::Pipes::Pipe' with identifier 'PipeBFF4E827-kvcogRY98bn1' did not stabilize. Status Reason is Input parameter is invalid from the request due to : Error occurred while sending mes
sage to SQS queue: arn:aws:sqs:eu-central-1::dlq" (RequestToken: 07f6ec0d-8398-4a70-f9db-4c2870efa33d, HandlerErrorCode: NotStabilized)

❌ cdk-aws-webhook-momento-dev failed: The stack named cdk-aws-webhook-momento-dev failed to deploy: UPDATE_ROLLBACK_COMPLETE: Resource handler returned message: "Resource of type 'AWS::Pipes::Pipe' with identifier 'PipeBFF4E827-kvcogRY98bn1' did not stabilize. Status Reason is Input parameter is invalid from the request due to : Error occurred while sending message to SQS queue: arn:aws:sqs:eu-central-1::dlq" (RequestToken: 07f6ec0d-8398-4a70-f9db-4c2870efa33d, HandlerErrorCode: NotStabilized)
👾 Task "deploy" failed when executing "cdk deploy" (cwd: /home/user/github/cdk-aws-webhook-momento)
```

### Reproduction Steps

See above.

### Possible Solution

_No response_

### Additional Information/Context

_No response_

### CDK CLI Version

2.161.1

### Framework Version

_No response_

### Node.js Version

20.18.0

### OS

Ubuntu 24.04

### Language

TypeScript

### Language Version

_No response_

### Other information

_No response_

Reproduce the failed update using the TypeScript example with DynamoDBSource, Pipe, SqsTarget, and deadLetterTarget enabled. Start by tracing how deadLetterTarget is handled for the AWS::Pipes::Pipe resource and compare the generated deployment configuration with the reported SQS stabilization error. Done means updating the stack succeeds with the dead-letter queue configured.

Written by the indexing model from the issue text.