feat(examples): chat-handler + production-trace-sink

[drewstone]

Summary

Two production patterns the prior nine examples did not cover — the most-asked-for missing pieces from the DX audit.

• examples/chat-handler/ — DurableChatTurnEngine.runTurn end-to-end. Builds the durable manifest from a chat identity (tenantId / sessionId / turnIndex), drives runDurableTurn, emits session.run.* lifecycle around the producer stream, returns the NDJSON ReadableStream the HTTP route forwards verbatim. Shows fresh and replay paths — turn 0 retried with the same identity hits the cached run without re-running the producer.
• examples/production-trace-sink/ — createProductionTraceSink wiring: a per-session TraceEmitter writes spans through the sink's TraceStore; on endRun the sink composes a canonical ProductionRunRecord and persists via your ProductionRunRecordStore (in-memory for the demo, Drizzle / D1 / Postgres in production). OTLP forwarding and recordFeedback are documented in the README.

Both runnable offline via pnpm tsx. The remaining gaps (PlatformAuthClient API tour, defineAgent end-to-end, D1DurableRunStore on real D1) are smaller and can land as follow-ons.

Test plan

• pnpm typecheck — 0 errors
• pnpm test — 251 passed (17 files)
• pnpm test:workers — 2 passed under real workerd
• pnpm exec biome check src tests examples — clean (2 pre-existing warnings)
• pnpm build — green
• Both new examples runnable: pnpm tsx examples/<dir>/<name>.ts

[tangletools]

Verified. Two missing production-pattern examples: chat-handler (DurableChatTurnEngine.runTurn end-to-end with fresh + replay paths) and production-trace-sink (per-session TraceEmitter + canonical RunRecord persistence). Both offline. typecheck 0, Node suite 251, workerd suite 2, biome clean, build green.