Fix Claude background task lifecycle UI

[brsbl]

Summary

Fixes three confirmed Claude background-task lifecycle failures:

• keeps open workflows/background commands visible in the latest timeline response even when their lifecycle row is outside the latest segment window
• shows the thread working indicator while an active background task is pending, even after the provider turn has completed and runtime status is idle
• makes Claude bridge same-session thread/resume idempotent so a reconnect/resume for the live provider session does not close the SDK session and stop background work

Root Cause Evidence

• Packaged-app DB evidence from the takeover thread showed Claude workflows commonly outlive their turn: 32 of 35 materialized Claude background tasks completed after the next turn/completed; one example completed roughly 39,974s after the turn completed. That confirms the shared lifecycle mismatch: turn done is not background work done.
• The latest timeline active-card projection was derived from selected timeline rows. If an open task started/progressed outside the latest segment, activeWorkflow / activeBackgroundCommands could be empty even though the task was still open.
• The spinner path only checked runtime display status. Claude turns go idle at turn/completed, so a still-running background workflow had no working indicator.
• Same-provider thread/resume previously closed an existing live Claude SDK session before starting/resuming, which could interrupt open background tasks.

Unverified/not changed here: subagent/monitor task materialization remains intentionally excluded by current filters, and quick completed tasks can still leave the active-card list immediately because active cards represent only pending tasks.

Changes

• Added a DB helper that returns the latest non-terminal lifecycle row for each open background task on a thread.
• Backfilled those open task rows into latest timeline responses for projection, using a thread-scoped progress snapshot when the only latest state is an old turn-scoped item/started.
• Updated the detail and timeline-panel working indicator to account for active background tasks.
• Added an idempotent Claude bridge resume path when the requested provider thread already has a live session.
• Added regression tests for the open-task timeline window gap, DB helper behavior, and same-session resume behavior.
• Added smoke coverage for both active-card surfaces: server route smoke for stale-window local_workflow and local_bash, plus app render smoke for background-only working indicators.

Validation

• pnpm exec turbo run test --filter=@bb/server
• pnpm exec turbo run test --filter=@bb/db
• pnpm exec turbo run test --filter=@bb/agent-runtime
• pnpm exec turbo run test --filter=@bb/app -- --run src/components/thread/timeline/ThreadTimelinePanelContent.test.tsx
• pnpm exec turbo run test --filter=@bb/server -- --run test/public/public-thread-data.test.ts -t "surfaces active"
• pnpm exec turbo run typecheck --filter=@bb/db
• pnpm exec turbo run typecheck --filter=@bb/server
• pnpm exec turbo run typecheck --filter=@bb/agent-runtime
• pnpm exec turbo run typecheck --filter=@bb/app