refactor(games): overhaul WS game system with improved UX and solo test support

Backend:
- Fix session never being attached to ws.data at upgrade time
- Add GameServer class: connection registry, per-connection room tracking,
  automatic room cleanup on disconnect via ws.data.rooms
- Replace ws-handler.ts with typed event-driven architecture using mitt
- Remove redundant subscription tracking from RoomManager
- Add JOIN_RESULT with player/spectator lists replacing error-as-control-flow
- Add SESSION_REPLACED for multi-tab same-account detection
- Add FILL_ROOM command for admin solo testing (fills empty slots with host)
- Fix dual-schema routing; remove game types from WsMessageSchema
- Per-player personalized views sent directly after each action

Chess plugin:
- Allow same-player (solo) mode: skip color/turn ownership checks
- Fix forfeit and disconnect handling in solo mode (winner: null)

Frontend:
- Click-to-move with legal move dots and last-move highlight
- Auto-scroll move history, forfeit confirmation, turn-reactive board border
- JOIN_RESULT initialises player/spectator lists immediately on join
- Contextual connecting state, player slot cards in waiting room
- Copy-invite button with Copied! flash, Back to Lobby CTA on finish
- Session-replaced warning banner with Rejoin here action
- Lobby passes preferAs intent through route state
- Admin waiting room shows Start Solo Test button

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

package.json

@@ -44,6 +44,7 @@
     "discord.js": "^14.25.1",
     "dotenv": "^17.2.3",
     "drizzle-orm": "^0.44.7",
+    "mitt": "^3.0.1",
     "postgres": "^3.4.8",
     "zod": "^4.3.6"
   }