chore: Align server-ai examples with EXAM-SDK-example spec

[jsonbailey]

Summary

Aligns the server-ai examples with the new EXAM-SDK-example spec, mirroring the patterns already landed in hello-python-ai (#27, #28) and improving on Python's config-key/env-var naming.

• Physical reorganization — examples/getting-started/{provider}/{method}/ and examples/features/{create-method}/; 10 examples down to 7 (observability examples folded in universally, chat-judge merged into create-model to match Python).
• Standardized config keys + env vars — LAUNCHDARKLY_COMPLETION_KEY/sample-completion, LAUNCHDARKLY_AGENT_KEY/sample-agent, LAUNCHDARKLY_AGENT_GRAPH_KEY/sample-agent-graph, LAUNCHDARKLY_JUDGE_KEY/sample-judge. Cleaner than Python's; will be back-ported in a follow-up hello-python-ai PR.
• Standardized output — init success line, sample-question framing, metric summary block (Duration, Success, token counts, Tool calls), judge result bullet format. Matches the Python format.
• Lifecycle — await ldClient.flush(); ldClient.close() in a finally block, everywhere. Several examples weren't flushing or closing before.
• Observability — @launchdarkly/observability-node wired into every example with a unique serviceName. Dedicated observability examples removed since the pattern is now universal.
• ESM + tsx — uniform module system; no per-example tsc step or dist/ output. Each example has a bootstrap script that builds only the SDK packages it depends on, so users don't need to build the whole monorepo.
• dotenv + .env.example — every example reads from a local .env and ships a .env.example documenting required vars.
• READMEs — top-level examples/README.md index with Getting Started / Features tables, and a 4-section per-example README (Prerequisites / Setup / Run, plus an "Adding judges" section on create-model).

No version bumps and no CHANGELOG changes — this is examples-only.

Test plan

• yarn install at repo root resolves cleanly
• npx tsc --noEmit passes for all 7 examples
• getting-started/openai/chat-completions runs end-to-end against an AI Config
• features/create-model runs end-to-end and prints judge results in the standardized format

---

Note

Low Risk
Examples-only restructuring plus CI/workspace config updates; main risk is broken example builds/type-checks or CI due to the new workspace names and path globbing.

Overview
Replaces the existing packages/sdk/server-ai/examples/* set with a smaller, reorganized set under examples/getting-started/... and examples/features/..., adding a top-level examples/README.md index and new per-example .env.example/README files.

Updates the example implementations to a consistent pattern: ESM + tsx execution, standardized env var/config key names (e.g. LAUNCHDARKLY_COMPLETION_KEY, LAUNCHDARKLY_AGENT_KEY, etc.), always wiring @launchdarkly/observability-node, printing a uniform metrics/judge-results summary, and ensuring flush()/close() happen in finally.

Adjusts repo plumbing to match: root package.json workspaces now point at the new example packages, and .github/workflows/server-ai.yml replaces per-example build steps with a globbed loop that focuses each example workspace, builds required dependencies, and runs tsc --noEmit.

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[github-actions]

@launchdarkly/js-sdk-common size report
This is the brotli compressed size of the ESM build.
Compressed size: 26208 bytes
Compressed size limit: 29000
Uncompressed size: 128789 bytes

[github-actions]

@launchdarkly/browser size report
This is the brotli compressed size of the ESM build.
Compressed size: 179498 bytes
Compressed size limit: 200000
Uncompressed size: 830837 bytes

[github-actions]

@launchdarkly/js-client-sdk size report
This is the brotli compressed size of the ESM build.
Compressed size: 31906 bytes
Compressed size limit: 34000
Uncompressed size: 113658 bytes

[github-actions]

@launchdarkly/js-client-sdk-common size report
This is the brotli compressed size of the ESM build.
Compressed size: 38487 bytes
Compressed size limit: 39000
Uncompressed size: 211236 bytes

[andrewklatzke]

Nit that may not be valid in these examples but LGTM