chore(vue-sdk): Add LDVueClient hardening, provider, plugin, and base composables

[joker23]

Note

Medium Risk
Touches core client init and subscription behavior used by all Vue apps; changes are defensive but affect when context/init callbacks fire and how start() rejects are surfaced.

Overview
Adds the Vue integration surface for LaunchDarkly: createLDProvider / createLDProviderWithClient, LDVuePlugin, and composables useLDClient and useInitializationStatus, with reactive context and init state via createReactiveInstance and optional initializing / failed provider slots.

LDVueClient is hardened so start() maps base rejections to a resolved { status: 'failed', error }, notifies context subscribers on complete/timeout (not only complete), and isolates getContext() and subscriber callback throws so one bad listener cannot break init or others. Provider/plugin support auto-start, deferInitialization, bootstrap merge (top-level wins), and custom injection keys for multi-env apps.

Public exports and package docs are updated; variation composables are deferred to a follow-up PR. Broad Jest coverage includes a shared makeMockClient helper.

^{Reviewed by Cursor Bugbot for commit 82337a3. 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: 26365 bytes
Compressed size limit: 29000
Uncompressed size: 129044 bytes

[github-actions]

@launchdarkly/js-client-sdk-common size report
This is the brotli compressed size of the ESM build.
Compressed size: 38739 bytes
Compressed size limit: 39000
Uncompressed size: 212244 bytes

[github-actions]

@launchdarkly/browser size report
This is the brotli compressed size of the ESM build.
Compressed size: 179579 bytes
Compressed size limit: 200000
Uncompressed size: 831422 bytes

[github-actions]

@launchdarkly/js-client-sdk size report
This is the brotli compressed size of the ESM build.
Compressed size: 31978 bytes
Compressed size limit: 34000
Uncompressed size: 114243 bytes

[joker23]

@cursor review

[joker23]

@cursor review

[cursor]

✅ Bugbot reviewed your changes and found no new issues!

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^{Reviewed by Cursor Bugbot for commit f64969a. Configure here.}

[joker23]

this case should really never happen, but we can use some extra handling in case the context is malformed.

[kinyoklion]

It would be good to move the test files per the Devin review comments.