Add PWA support with manifest, service worker, and install prompt

[yuliuyi717-ux]

Related to #42

This PR implements PWA support and install UX for the frontend.

What's included:

1. Web app manifest
   • public/manifest.json
   • includes app metadata, theme/background colors, standalone display mode, and icons
2. Service worker for offline capability
   • public/sw.js
   • caches static assets and navigation responses to support offline access for previously visited pages
3. Install prompt banner
   • new src/components/InstallPrompt.tsx
   • handles beforeinstallprompt and appinstalled lifecycle
4. Layout wiring
   • src/app/layout.tsx now references manifest metadata and renders install prompt
5. Next.js service worker delivery headers
   • next.config.js adds headers for /sw.js and /manifest.json

TDD-style checks used:

• RED checks: missing manifest, missing SW config/registration, missing install prompt
• GREEN checks: all required artifacts added and wired in layout/config

Note: full app build/lint was not run in this environment because dependency installation requires monorepo workspace resolution (workspace:*).