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>

bun.lock

@@ -10,6 +10,7 @@
         "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",
       },
@@ -453,6 +454,8 @@
 
     "magic-string": ["magic-string@0.30.21", "", { "dependencies": { "@jridgewell/sourcemap-codec": "^1.5.5" } }, "sha512-vd2F4YUyEXKGcLHoq+TEyCjxueSeHnFxyyjNp80yg0XV4vUhnDer/lvvlqM/arB5bXQN5K2/3oinyCRyx8T2CQ=="],
 
+    "mitt": ["mitt@3.0.1", "", {}, "sha512-vKivATfr97l2/QBCYAkXYDbrIWPM2IIKEl7YPhjCvKlG3kE2gm+uBo6nEXK3M5/Ffh/FLpKExzOQ3JJoJGFKBw=="],
+
     "ms": ["ms@2.1.3", "", {}, "sha512-6FlzubTLZG3J2a/NVCAleEhjzq5oxgHyaCU9yYXvcLsvoVaHJq/s5xXI6/XXP6tz7R9xAOtHnSO/tXtF3WRTlA=="],
 
     "nanoid": ["nanoid@3.3.11", "", { "bin": { "nanoid": "bin/nanoid.cjs" } }, "sha512-N8SpfPUnUp1bK+PMYW8qSWdl9U+wwNWI4QKxOYDy9JAro3WMX7p2OeVRF9v+347pnakNevPmiHhNmZ2HbFA76w=="],