feat: wire activity feed to real api data (Closes #822)

[liufang88789-ui]

Replaces the home page activity feed mock data with a real API-backed query and keeps the UX resilient when the activity endpoint is unavailable.

Highlights:

• adds GET /api/activity integration via api/activity.ts
• adds useActivity() hook with 30s auto-refresh
• supports real activity events from the backend
• shows No recent activity for empty responses
• gracefully falls back to demo activity when the API is unavailable
• keeps the component self-contained and lightweight for the home page

Validation:

• npm test -- --run src/__tests__/activity-feed-home.test.tsx ✅

Closes #822

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