@amzn/synthetics-playwright: Make @amzn/synthetics-playwright public available?

### Describe the feature

Make `@amzn/synthetics-playwright` publicly available used for developing AWS Synthetics Node.js based canaries:

https://docs.aws.amazon.com/AmazonCloudWatch/latest/monitoring/Synthetics_WritingCanary_Nodejs_Playwright.html

### Use Case

Based on:

https://docs.aws.amazon.com/AmazonCloudWatch/latest/monitoring/Synthetics_WritingCanary_Nodejs_Playwright.html

I am using: `@amzn/synthetics-playwright` to write some AWS Synthetics Node.js canaries:

```
import { synthetics } from '@amzn/synthetics-playwright';
import { expect } from '@playwright/test';

export const handler = async () => {
try {
// Launch a browser
const browser = await synthetics.launch();

// Create a new page
const page = await synthetics.newPage(browser);
```

I have not been able to find the '@amzn/synthetics-playwright` anywhere and this indicates its not publicly available https://github.com/guardian/consent-management-platform/blob/7c41ee4929bd5ad9ff4f03c699f09103709d9ba1/synthetics/src/index.js#L1

Is there a change this package could be made publicly available to increase developer experience when writing Node.js canary handlers?

### Proposed Solution

_No response_

### Other Information

_No response_

### Acknowledgements

- [ ] I may be able to implement this feature request
- [ ] This feature might incur a breaking change

### AWS CDK Library version (aws-cdk-lib)

2.201.0

### AWS CDK CLI version

2.1018.1

### Environment details (OS name and version, etc.)

macOS 15.6

Start by reviewing the linked AWS Synthetics Playwright documentation and the existing references to @amzn/synthetics-playwright. Determine what public-package change is required and where it belongs in the aws-cdk project; done means the package is publicly available for the documented Node.js canary workflow.

Written by the indexing model from the issue text.