chore: Add example for LangChain provider integration

[jsonbailey]

Note

Adds a new packages/sdk/server-ai/examples/langchain-chat example demonstrating AI chat with LaunchDarkly AI SDK and LangChain, and registers it in workspaces.

• Examples:
  • New packages/sdk/server-ai/examples/langchain-chat:
    • src/index.ts: Initializes LaunchDarkly, sets up AI chat via initAi().initChat(...), and invokes a sample conversation.
    • package.json: Adds LangChain and LaunchDarkly AI dependencies; start script builds and runs.
    • README.md: Setup instructions, env vars, and sample AI Config.
    • tsconfig.json: TS build config for the example.
• Repo config:
  • Add example path to root package.json workspaces array.

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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: 24988 bytes
Compressed size limit: 26000
Uncompressed size: 122411 bytes

[github-actions]

@launchdarkly/js-client-sdk size report
This is the brotli compressed size of the ESM build.
Compressed size: 21721 bytes
Compressed size limit: 25000
Uncompressed size: 74698 bytes

[github-actions]

@launchdarkly/js-client-sdk-common size report
This is the brotli compressed size of the ESM build.
Compressed size: 17636 bytes
Compressed size limit: 20000
Uncompressed size: 90259 bytes

[jsonbailey]

The build will fail until we deploy the langchain-provider package.