feat: implement waitForInitialization for browser sdk 4.x

[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

• feat: adding waitForInitialize to browser 4.x
• test: adding unit tests for waitForInitilization

Describe the solution you've provided

Added waitForInitialization function to browser 4.x implementation.

Additional context

• I kept the method signiture the same as 3.x but am open to updating it to align with what we have in the server sdks f({timeout: 5}) instead of f(5)
• I "simplified" the way we are tracking for the initialization state to a boolean. It looks like our new identification would not be throwing which minimizes the reject conditions... I can add those back in case we get an error status returned? At that point we might want to just wait for the timeout to throw.
• I put in a default 5 seconds timeout on the wait
• I also added in an initialized event that a successful identify will emit, I figured that would be a way for developers to know if LDClient initialized even if the initialization goes past timeout.

---

Note

Adds waitForInitialization({ timeout }) to the browser SDK, resolves on identify success/failure or timeout, and emits an initialized event; includes comprehensive tests.

• Browser SDK 4.x
  • New API: LDClient.waitForInitialization(options?: { timeout: number }) returning LDWaitForInitializationResult (complete | failed | timeout).
  • Initialization flow:
    • Tracks init state via internal promise and result cache in BrowserClientImpl.
    • Resolves to complete on successful identify, failed on identify error, or timeout via cancelableTimedPromise.
    • Exposes waitForInitialization on returned client from makeClient.
  • Types: Adds LDWaitForInitializationOptions, LDWaitForInitializationComplete|Failed|Timeout and union LDWaitForInitializationResult in packages/sdk/browser/src/LDClient.ts.
• Events
  • Emits initialized on successful identify in shared LDClientImpl.
  • Expands emitter EventName to include initialized.
• Compat
  • compat/LDClientCompat omits waitForInitialization from its interface to preserve 3.x surface.
• Tests
  • Adds unit tests covering: blocking until ready, timeout behavior, immediate failure resolution, and failure-before-wait handling.

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[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 size report
This is the brotli compressed size of the ESM build.
Compressed size: 22427 bytes
Compressed size limit: 25000
Uncompressed size: 77390 bytes

[github-actions]

@launchdarkly/js-client-sdk-common size report
This is the brotli compressed size of the ESM build.
Compressed size: 17645 bytes
Compressed size limit: 20000
Uncompressed size: 90305 bytes