fix(performance): implement persistent caching and fix modal z-index

Performance Improvements:
- Add Zustand persist middleware for localStorage caching
- Implement cache TTL (5 minutes) for app list data
- Use stale-while-revalidate pattern for instant UI load
- Non-blocking initialization: setTimeout for all data fetching
- Smart loading state: only shows spinner if no cached data

UI Fixes:
- Fix AppDetailSheet overlapping bottom navbar
- Increase modal z-index from 100 to 999

This fixes the critical issue where app was VERY slow on restart,
reloading everything from scratch. Now app shows cached data
instantly and refreshes in background.

Author: risunCode