test(js-client-sdk): adding hello app test

[joker23]

Requirements

• I have added test coverage for new or changed functionality
• I have followed the repository's pull request submission guidelines
• I have validated my changes against all supported platform versions

Related issues

sdk-1910

Describe the solution you've provided

added the test

Additional context

I deviated a bit from the specs and read the flag value from the UI. I think we should update the specs to include this as a way to verify.

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Note

Medium Risk
Changes CI behavior and introduces a new job that pulls secrets via OIDC/AWS SSM and runs browser automation, which can add flakiness and requires correct permissions/configuration.

Overview
Adds a lightweight Playwright e2e smoke test for @launchdarkly/browser-example that loads the built static page and asserts the UI reports the boolean flag evaluates to true.

Updates the sdk/browser GitHub Actions workflow to run nightly on a cron schedule and introduces a new run-example job that fetches LaunchDarkly keys from AWS SSM, builds the example, installs Chromium, and executes the new Playwright tests (while skipping the existing browser build/test matrix on scheduled runs).

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[github-actions]

@launchdarkly/js-sdk-common size report
This is the brotli compressed size of the ESM build.
Compressed size: 25566 bytes
Compressed size limit: 26000
Uncompressed size: 125383 bytes

[github-actions]

@launchdarkly/browser size report
This is the brotli compressed size of the ESM build.
Compressed size: 171694 bytes
Compressed size limit: 200000
Uncompressed size: 799867 bytes

[github-actions]

@launchdarkly/js-client-sdk size report
This is the brotli compressed size of the ESM build.
Compressed size: 23845 bytes
Compressed size limit: 25000
Uncompressed size: 82750 bytes

[github-actions]

@launchdarkly/js-client-sdk-common size report
This is the brotli compressed size of the ESM build.
Compressed size: 20569 bytes
Compressed size limit: 24000
Uncompressed size: 107197 bytes