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
Changes the public initialization-state contract by removing the unknown state and adjusting when context-change subscribers are notified, which could affect apps gating rendering on the previous state transitions.

Overview
Unifies initialization state handling by removing the unknown state and treating clients as initializing until start() resolves (InitializedState and useInitializationStatus updated accordingly).

Refactors LDReactClient.start() semantics to be explicitly idempotent via internal guards and to notify onContextChange subscribers once after the first successful start() completion; identify() reuses the same notification path.

Updates mocks, tests, and migration docs to reflect the new initial status (initializing) and the dropped unknown branch.

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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/js-client-sdk size report
This is the brotli compressed size of the ESM build.
Compressed size: 24546 bytes
Compressed size limit: 25000
Uncompressed size: 85156 bytes

[github-actions]

@launchdarkly/js-client-sdk-common size report
This is the brotli compressed size of the ESM build.
Compressed size: 22203 bytes
Compressed size limit: 24000
Uncompressed size: 115238 bytes

[github-actions]

@launchdarkly/browser size report
This is the brotli compressed size of the ESM build.
Compressed size: 172365 bytes
Compressed size limit: 200000
Uncompressed size: 802275 bytes

[devin-ai-integration]

✅ Devin Review: No Issues Found

Devin Review analyzed this PR and found no potential bugs to report.

View in Devin Review to see 5 additional findings.

[joker23]

@cursor review

[joker23]

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[cursor]

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