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>

shared/modules/dashboard/dashboard.types.ts

@@ -104,17 +104,12 @@ export const MaintenanceModeSchema = z.object({
     reason: z.string().optional(),
 });
 
-// WebSocket Message Schemas
+// WebSocket Message Schemas (dashboard messages only — game messages live in api/src/games/types.ts)
 export const WsMessageSchema = z.discriminatedUnion("type", [
     z.object({ type: z.literal("PING") }),
     z.object({ type: z.literal("PONG") }),
     z.object({ type: z.literal("STATS_UPDATE"), data: DashboardStatsSchema }),
     z.object({ type: z.literal("NEW_EVENT"), data: RecentEventSchema }),
-    // Game messages (client → server)
-    z.object({ type: z.literal("CREATE_ROOM"), gameType: z.string() }),
-    z.object({ type: z.literal("JOIN_ROOM"), roomId: z.string(), as: z.enum(["player", "spectator"]) }),
-    z.object({ type: z.literal("LEAVE_ROOM"), roomId: z.string() }),
-    z.object({ type: z.literal("GAME_ACTION"), roomId: z.string(), action: z.record(z.unknown()) }),
 ]);
 
 export type WsMessage = z.infer<typeof WsMessageSchema>;