Add OpenTelemetry distributed tracing example for Azure Managed DTS

[torosent]

Summary

What changed?

• Added a new distributed-tracing.ts example in examples/azure-managed/ that demonstrates end-to-end OpenTelemetry distributed tracing with the Durable Task JavaScript SDK
• Added a docker-compose.yml that starts the DTS Emulator (mcr.microsoft.com/dts/emulator:latest) and Jaeger for local trace visualization
• Added .env.emulator with pre-configured connection string for the local emulator
• Added a comprehensive README.md with step-by-step setup instructions for both emulator and cloud scenarios
• Renamed connection string env var from AZURE_DTS_CONNECTION_STRING to DURABLE_TASK_SCHEDULER_CONNECTION_STRING across examples and E2E tests
• Fixed type annotation issue with Task<Promise<T>> vs Task<T> in index.ts fan-out example

Why is this change needed?

• Users need a working example showing how to enable and visualize distributed traces for durable orchestrations
• The SDK already supports OpenTelemetry tracing (via optional peer dependency), but there was no example demonstrating how to set it up with a trace collector
• The DTS Emulator Docker image enables local development without an Azure subscription

Issues / work items

• Related: Distributed tracing support for JavaScript SDK

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Project checklist

• Release notes are not required for the next release
• Backport is not required
• All required tests have been added/updated (unit tests, E2E tests)
• Breaking change?
  • No breaking changes. Only additions (new example files) and env var rename in examples/tests.

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AI-assisted code disclosure (required)

Was an AI tool used? (select one)

• No
• Yes, AI helped write parts of this PR (e.g., GitHub Copilot)
• Yes, an AI agent generated most of this PR

If AI was used:

• Tool(s): GitHub Copilot (VS Code agent mode)
• AI-assisted areas/files: distributed-tracing.ts, docker-compose.yml, .env.emulator, README.md
• What you changed after AI output: Reviewed and verified all OTel SDK usage, connection string patterns, and DTS emulator image reference

AI verification (required if AI was used):

• I understand the code and can explain it
• I verified referenced APIs/types exist and are correct
• I reviewed edge cases/failure paths (timeouts, retries, cancellation, exceptions)
• I reviewed concurrency/async behavior
• I checked for unintended breaking or behavior changes

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Testing

Automated tests

• Result: Existing unit tests pass. This PR adds example code only (no new unit tests needed).

Manual validation (only if runtime/behavior changed)

• Environment (OS, Node.js version, components): macOS, Node.js 22, Docker
• Steps + observed results:
  1. docker compose up -d — DTS Emulator + Jaeger started
  2. cp .env.emulator .env — configured for local emulator
  3. npm run example -- ./examples/azure-managed/distributed-tracing.ts — both orchestrations completed
  4. Opened Jaeger UI at http://localhost:16686 — traces visible under service durabletask-js-tracing-example

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Notes for reviewers

• The OTel packages (@opentelemetry/sdk-node, etc.) are not added to package.json — they are installed ad-hoc with npm install --no-save as documented in the README, keeping the repo dependency footprint small.
• The DTS Emulator image is mcr.microsoft.com/dts/emulator:latest with Authentication=None for local dev.

[Copilot]

Pull request overview

This PR adds OpenTelemetry distributed tracing support to the Durable Task JavaScript SDK for Azure Managed DTS. It enables end-to-end trace visualization across orchestration scheduling, execution, activities, sub-orchestrations, and timers through W3C Trace Context propagation.

Changes:

• Added comprehensive OpenTelemetry tracing infrastructure with optional peer dependency on @opentelemetry/api
• Introduced structured logging system with event IDs and categories matching .NET SDK conventions
• Renamed environment variable from AZURE_DTS_CONNECTION_STRING to DURABLE_TASK_SCHEDULER_CONNECTION_STRING across examples and tests
• Added distributed tracing example with DTS Emulator and Jaeger visualization setup

Reviewed changes

Copilot reviewed 40 out of 41 changed files in this pull request and generated no comments.

Show a summary per file

File	Description
packages/durabletask-js/src/tracing/*	New tracing infrastructure including constants, trace context utilities, and helper functions for span creation
packages/durabletask-js/src/worker/*	Integration of tracing spans and structured logging into worker execution flow
packages/durabletask-js/src/client/*	Integration of tracing spans and structured logging into client operations
packages/durabletask-js/src/types/logger.type.ts	Added StructuredLogger interface and createLogEventHandler for structured logging
packages/durabletask-js/src/utils/*	New utility functions for error handling and log emission
packages/durabletask-js/test/*	Comprehensive test coverage for tracing and logging features
examples/azure-managed/distributed-tracing.ts	New example demonstrating OpenTelemetry tracing with Jaeger
examples/azure-managed/docker-compose.yml	Docker setup for DTS Emulator and Jaeger
test/e2e-azuremanaged/*.spec.ts	Updated E2E tests with new connection string environment variable
packages/durabletask-js/package.json	Added OpenTelemetry as optional peer dependency

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