chore: add an example app for browser sdk

[joker23]

This PR will add a new browser SDK example that works with the new 4.x implementation.

I think this also addressed sdk-744

---

Note

Adds a new browser example app for the JS client SDK and includes it in the monorepo workspaces.

• Example app (packages/sdk/browser/example):
  • Client demo (src/app.ts): initializes @launchdarkly/js-client-sdk, identifies a user context, evaluates flagKey via variation, listens for change/error, and updates page text/background accordingly.
  • Build/setup: adds package.json with tsdown build and start scripts; includes tsconfig.json and tsdown.config.ts targeting browser; simple index.html and index.css for rendering.
• Monorepo:
  • Adds packages/sdk/browser/example to root package.json workspaces list.

^{Written by Cursor Bugbot for commit 22f3a41. This will update automatically on new commits. Configure here.}

[github-actions]

@launchdarkly/browser size report
This is the brotli compressed size of the ESM build.
Compressed size: 169118 bytes
Compressed size limit: 200000
Uncompressed size: 789399 bytes

[github-actions]

@launchdarkly/js-sdk-common size report
This is the brotli compressed size of the ESM build.
Compressed size: 25394 bytes
Compressed size limit: 26000
Uncompressed size: 124693 bytes

[github-actions]

@launchdarkly/js-client-sdk-common size report
This is the brotli compressed size of the ESM build.
Compressed size: 17636 bytes
Compressed size limit: 20000
Uncompressed size: 90259 bytes

[github-actions]

@launchdarkly/js-client-sdk size report
This is the brotli compressed size of the ESM build.
Compressed size: 22101 bytes
Compressed size limit: 25000
Uncompressed size: 76263 bytes

[cursor]

Bug: UI remains stuck when identify succeeds without flags

The identify call only has a .catch() handler without a .then() for the success case. The UI update relies entirely on the change event firing. However, the SDK only emits a change event when flag values differ from previous values. If no flags are configured in the LaunchDarkly project (or the server returns empty flags), identify succeeds but no change event fires, leaving the UI permanently stuck on "Initializing...". Adding a .then() handler that calls render() would ensure the UI updates after successful identification regardless of whether flags exist.

 

[cursor]

Bug: Identify error handling uses catch but promise never rejects

The .catch() handler on ldclient.identify(context) will never execute because the SDK's identify() method returns a promise that doesn't reject on errors. Per the SDK's documented behavior, the promise "will not be rejected" - instead, errors are returned as an LDIdentifyResult object with status: 'error'. To properly handle identify failures, the code would need to use .then() and check result.status for error conditions.