Studio chat: live subagent, parallel, and team activity

Parent: #1736. Design review: #1779.
Design baseline: 2026-09-24.

Outcome

Delegated work is legible while a run is live and after its events settle.

Model the distinct subagent.*, parallel.*, and team.* event families separately in the browser's provider-neutral event projection; show inline cards and a session-level activity panel.
Show child state, tool summaries, branch winners, team roster/tasks/findings, stop reason, and bounded trace previews when those facts exist. Treat model-influenced text as plain text, not HTML or trusted Markdown.
Do not offer per-child cancellation unless the published SDK and BFF expose a real per-child control; whole-run cancellation remains separate.

Interleaved and replayed delegation events produce stable cards for all three families, including failed and completed states, without conflating a parallel branch with a subagent.
The panel is keyboard accessible and responsive; no browser code imports the SDK or daemon protocol types.
Reducer/component proofs and task studio:check pass, with a browser journey coordinated through Studio test coverage: Playwright journeys, apps/web unit gaps, CI job #1776.

Bounded; review the existing event projection before declaring any BFF contract additions.

Depends on: #1847.