aws-cognito: Invalid write attribute for client

### Describe the bug

Creating a writeable custom attribute on a User Pool Client results in an error when deploying.

### Expected Behavior

Custom attributes are able to be made writeable in User Pool Clients just like standard attributes are.

### Current Behavior

Error output from `deploy` command:

```
8:37:09 AM | CREATE_FAILED | AWS::Cognito::UserPoolClient | LocalUserPoolEncoreClientD9A7741D
Invalid write attributes specified while creating a client (Service: AWSCognitoIdentityProviderService; Status Code: 400; Error Code: InvalidParameterException; Request ID: ef50ac13-2935-4fc2-91e4-216daad7f183; Proxy: null)

❌ EncoreStack-local failed: Error: The stack named EncoreStack-local failed creation, it may need to be manually deleted from the AWS console: ROLLBACK_COMPLETE: Invalid write attributes specified while creating a client (Service: AWSCognitoIdentityProviderService; Status Code: 400; Error Code: InvalidParameterException; Request ID: ef50ac13-2935-4fc2-91e4-216daad7f183; Proxy: null)
at prepareAndExecuteChangeSet (/Users/jackson/dev/enc-perf-web/cdk/node_modules/aws-cdk/lib/api/deploy-stack.ts:385:13)
at processTicksAndRejections (node:internal/process/task_queues:96:5)
at CdkToolkit.deploy (/Users/jackson/dev/enc-perf-web/cdk/node_modules/aws-cdk/lib/cdk-toolkit.ts:209:24)
at initCommandLine (/Users/jackson/dev/enc-perf-web/cdk/node_modules/aws-cdk/lib/cli.ts:341:12)

The stack named EncoreStack-local failed creation, it may need to be manually deleted from the AWS console: ROLLBACK_COMPLETE: Invalid write attributes specified while creating a client (Service: AWSCognitoIdentityProviderService; Status Code: 400; Error Code: InvalidParameterException; Request ID: ef50ac13-2935-4fc2-91e4-216daad7f183; Proxy: null)
```

### Reproduction Steps

Create an instance of this class as part of a `Stack`

```js
export class EncoreUserPool extends Construct {
readonly userPool: cognito.UserPool;
readonly userPoolClient: cognito.UserPoolClient;

constructor(scope: Construct, id: string, props: EncoreUserPoolProps) {
super(scope, id);

this.userPool = new cognito.UserPool(this, "UserPool", {
// ...rest
standardAttributes: {
email: { required: true, mutable: true },
},
customAttributes: {
existsInDjango: new cognito.StringAttribute({ mutable: true }),
},
});

// source of the error
const clientWriteAttributes = new cognito.ClientAttributes().withCustomAttributes("existsInDjango");

const clientReadAttributes = clientWriteAttributes.withStandardAttributes(
// some standard attributes here
);

this.userPoolClient = this.userPool.addClient("ClientPool", {
// ...rest
readAttributes: clientReadAttributes,
writeAttributes: clientWriteAttributes,
});
}
}
```

### Possible Solution

_No response_

### Additional Information/Context

The User Pool is being created no problem, the issues arises from trying to make the `existsInDjango` custom attribute writeable. Stack deploys just fine when that line is not included.

### CDK CLI Version

2.28.0

### Framework Version

aws-cdk@2.28.0

### Node.js Version

16.13.1

### OS

macOS 12.4

### Language

Typescript

### Language Version

typescript@3.9.10

### Other information

_No response_

Start by tracing ClientAttributes.withCustomAttributes and UserPool.addClient in the CDK Cognito implementation to see how custom write attributes are synthesized. Reproduce the issue with the provided TypeScript construct and confirm that deployment succeeds when the mutable custom attribute is included in writeAttributes.

Written by the indexing model from the issue text.