(orchestration): Sync task context into operator IDE workspaces

## Component

API or orchestration

## Describe the feature

When a background task is running or recently updated, expose a **machine-readable context bundle** (summary, evidence links, relevant file paths, branch name, latest milestones) that IDE plugins or local agent configs can poll—so engineers debugging alongside the task do not re-read Slack/GitHub manually.

## Use case

Responders and tech leads often work in an IDE while a background agent runs elsewhere. Copy-pasting status from notifications is friction. A stable, low-latency context endpoint enables **side-by-side collaboration** without turning every task into a live pair-programming session.

## Proposed solution

1. `GET /tasks/{id}/workspace-context` returning JSON: `branch`, `repo`, `summary`, `milestones[]`, `open_questions[]`, `hydration_digest` (bounded).
2. Optional MCP tool or documented `bgagent context export --task-id` for local agents.
3. Auth same as `GET /tasks/{id}`; rate-limited.
4. Align fields with roadmap **Smart progress updates** event schema to avoid duplication.

## Other information

- Does not require hosting a shared cloud IDE session—local consumption only in v1.
- Browser extension channel (roadmap) may consume the same payload.

## Acknowledgements

- [ ] I may be able to implement this feature
- [ ] This might be a breaking change

## Acceptance criteria

- [ ] Endpoint documented in `API_CONTRACT.md`; types in `cli/src/types.ts`.
- [ ] CLI export command writes JSON to stdout or file.
- [ ] Payload size capped; large traces remain on S3 trace URI.
- [ ] Handler tests cover running and terminal tasks.

Start with API_CONTRACT.md and cli/src/types.ts, then inspect the existing GET /tasks/{id} handler and the Smart progress updates event schema for authentication and field alignment. Add the documented context endpoint, CLI JSON export, bounded payload behavior, and tests covering running and terminal tasks; done means all acceptance criteria pass.

Written by the indexing model from the issue text.