(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.

Commencez par API_CONTRACT.md et cli/src/types.ts, puis examinez le handler existant de GET /tasks/{id} ainsi que le schéma d’événements de Smart progress updates pour vérifier l’authentification et l’alignement des champs. Ajoutez l’endpoint de contexte documenté, l’export JSON de la CLI, le comportement avec une payload limitée et des tests couvrant les tâches en cours d’exécution et les tâches dans un état terminal ; le travail est terminé lorsque tous les critères d’acceptation sont satisfaits.