feat: all screens built — chess lobby, profile, leaderboard, friends, shop, achievements, settings, ludo/domino/backgammon lobbies

Phase 2+3 complete:
- Chess lobby: full time control picker, bot selector, multiplayer search
- Chess game: wraps Board + Game engines in immersive mode
- Ludo lobby: player count, bot difficulty, room codes
- Domino lobby: 2P/4P teams, difficulty, room codes
- Backgammon lobby: match length, room codes
- Profile: XP bar, per-game ratings, economy, stats
- Leaderboard: multi-game + multi-mode selector
- Friends: list, requests, search, add
- Shop: categories, buy with coin burst particles, equip
- Achievements: grid with progress tracking
- Settings: sound toggle, logout
- Fix: router import bug in main.js
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>