refactor: simplify getting initializationState

[joker23]

This PR will align our initialization status handling closer to the base browser sdk by:

• combining initializing and unknown state which should get rid of one extra state dispatch on initialization
• adding additional idempotent guards to the start function. Note that these are redundant protections.

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Note

Medium Risk
Medium risk because it changes the public initialization-state contract (dropping unknown) and alters server-side/noop client behavior to return a failure + error, which may affect consumers that previously treated these as non-error states.

Overview
Initialization state handling is simplified by removing the unknown state from InitializedState/InitializationStatus and defaulting new clients and test harnesses to initializing.

createClient() behavior changes: start() now uses explicit idempotency guards (startCalled/startNotified) and triggers a one-time onContextChange notification after the first successful start() completion; the server-side/noop client now reports failed with a concrete getInitializationError() message instead of returning unknown/undefined.

Tests and the migration docs are updated to reflect the new state model and server-side error semantics.

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[github-actions]

@launchdarkly/js-sdk-common size report
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Uncompressed size: 126143 bytes

[github-actions]

@launchdarkly/js-client-sdk size report
This is the brotli compressed size of the ESM build.
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Uncompressed size: 86916 bytes

[github-actions]

@launchdarkly/js-client-sdk-common size report
This is the brotli compressed size of the ESM build.
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Uncompressed size: 156220 bytes

[github-actions]

@launchdarkly/browser size report
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Uncompressed size: 804043 bytes

[devin-ai-integration]

✅ Devin Review: No Issues Found

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[joker23]

@cursor review

[joker23]

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[kinyoklion]

Should these be ran in another turn of the event loop? Or do we want them inline.

Basically do you want the result of the identify before the context notification, or after?

[joker23]

I think we can only notify after the identify promise is resolved... I don't think we can really inline this as we are using the browser sdk identify method.