fix(prime): make child live activity truthful

[rynfar]

Problem

Prime child agents can be actively thinking or using tools while the privacy-bounded Live activity stream contains no assistant text. The web and mobile empty state described that as no assistant activity, and invisible watcher events could exhaust the bounded initialization buffer before any renderable update arrived.

Fix

• present the safe status aggregates already visible in the agent roster while labeling an empty snapshot as No assistant text yet
• explain that tool arguments, results, and reasoning remain hidden, with matching web and mobile behavior
• discard watcher events that cannot change the sanitized public snapshot before initialization admission
• document Prime 0.7.2's attach-time streaming limitation without relying on private APIs

Verification

• vp test run apps/server/src/provider/prime/PrimeAgentDaemonSessionRuntime.test.ts apps/web/src/components/AgentsPanel.test.tsx packages/client-runtime/src/state/sessionAgentLiveActivity.test.ts apps/mobile/src/features/threads/sessionAgentMenu.test.ts — 78 tests passed
• targeted lint passed for every changed TypeScript/TSX file
• server, web, client-runtime, and mobile typechecks passed
• two independent code reviews completed with no remaining findings
• integrated web verification passed for the truthful empty snapshot and long-content overflow state; the activity region scrolls while the footer remains visible
• integrated iOS Simulator verification passed for the same safe summary, empty-state copy, and privacy explanation
• the iOS pass exposed two unrelated pre-existing mobile thread runtime errors; their isolated correction is PR fix(mobile): remove stray composer text #32

Model: GPT-5.6; Harness: Prime Agent.

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[github-actions]

Thread transfer impact

⚠️ The latest CI run did not produce a thread transfer result for 215771e.

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