fix(dashboard): surface lifecycle status updates in chat sidebar

[LeonSGP43]

Fixes #37185.

Summary

• surface status.update events in the dashboard chat sidebar instead of silently dropping them
• keep a small deduplicated lifecycle/status feed next to the existing tool feed
• widen the events-feed disconnect warning so it covers both tool and status updates

Notes

The original issue body points at a missing status_callback, but current origin/main already carries PTY-side event mirroring through /api/pub and /api/events. The remaining user-visible bug on latest main is in web/src/components/ChatSidebar.tsx, which only handled tool.start/progress/complete and ignored incoming status.update frames.

Proof

• cd web && ./node_modules/.bin/eslint src/components/ChatSidebar.tsx
• cd web && npm run build
• git diff --check