feat: adding start() method to common client sdk package

[joker23]

This PR will consolidate the start() method into the shared client sdk package.

To do this we also:

• introduce an internal option called requiresStart which should be true for new SDKs (and only RN has it default false)
• requiresStart is, effectively, a feature flag for whether the SDK is using the new create + start initialization pattern
• consolidated the unit tests for the start method into client common
• moved start method out of browser and electron sdks

---

Note

Medium Risk
Touches core client initialization and identify queuing semantics across browser/electron, which could affect startup and context switching behavior. Changes are mostly consolidation but impact widely used lifecycle paths (bootstrap, timeouts, sheddable identifies).

Overview
Consolidates the client start() implementation into the shared sdk-client LDClientImpl, including bootstrap flag preloading, cached/idempotent start() promises, and integration with waitForInitialization timeouts.

Introduces an internal requiresStart option that gates a new lifecycle: when enabled (now set to true in Browser and Electron), identify calls before start() return an error result, and post-start identifyResult defaults sheddable to true when not explicitly provided.

Removes duplicated start()/pre-start identify logic from the Browser and Electron clients, updates their public LDStartOptions types to extend the common LDStartOptions, and moves/rewrites unit tests so start/bootstrapping/guard behavior is validated centrally (with browser/electron tests trimmed accordingly).

^{Reviewed by Cursor Bugbot for commit d249ad8. Bugbot is set up for automated code reviews on this repo. Configure here.}

[github-actions]

@launchdarkly/js-sdk-common size report
This is the brotli compressed size of the ESM build.
Compressed size: 25661 bytes
Compressed size limit: 29000
Uncompressed size: 126143 bytes

[github-actions]

@launchdarkly/browser size report
This is the brotli compressed size of the ESM build.
Compressed size: 179455 bytes
Compressed size limit: 200000
Uncompressed size: 829373 bytes

[github-actions]

@launchdarkly/js-client-sdk size report
This is the brotli compressed size of the ESM build.
Compressed size: 31603 bytes
Compressed size limit: 34000
Uncompressed size: 112189 bytes

[github-actions]

@launchdarkly/js-client-sdk-common size report
This is the brotli compressed size of the ESM build.
Compressed size: 37458 bytes
Compressed size limit: 38000
Uncompressed size: 205781 bytes

[joker23]

@cursor review

[cursor]

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^{Reviewed by Cursor Bugbot for commit d249ad8. Configure here.}