feat(games): implement chess game plugin with full UI

Add chess as the first game plugin using the existing multiplayer framework.
Server-side game logic uses chess.js with server-authoritative clock management.
Client uses react-chessboard v5 with cburnett piece set, drag-and-drop + click-to-move,
configurable time controls (bullet/blitz/rapid/classical/none), draw offers,
resignation, and timeout detection. Extends the game framework with room creation
options to support per-game configuration. Includes 57 tests covering all code paths.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

api/src/games/RoomManager.ts

@@ -33,7 +33,7 @@ export class RoomManager {
     private cleanupTimers = new Map<string, Timer>();
     readonly emitter = mitt<RoomEvents>();
 
-    createRoom(gameSlug: string, hostId: string): CreateResult {
+    createRoom(gameSlug: string, hostId: string, options?: Record<string, unknown>): CreateResult {
         const plugin = gameRegistry.get(gameSlug);
         if (!plugin) return { ok: false, error: `Unknown game type: ${gameSlug}` };
 
@@ -47,6 +47,7 @@ export class RoomManager {
             state: null,
             status: "waiting",
             createdAt: Date.now(),
+            options,
         };
 
         this.rooms.set(id, room);
@@ -85,7 +86,7 @@ export class RoomManager {
         room.players.push(playerId);
 
         if (room.players.length >= plugin.maxPlayers) {
-            room.state = plugin.createInitialState(room.players);
+            room.state = plugin.createInitialState(room.players, room.options);
             room.status = "playing";
             this.scheduleCleanup(roomId, ROOM_CONFIG.PLAYING_MAX_MS);
 
@@ -185,7 +186,7 @@ export class RoomManager {
             room.players.push(adminId);
         }
 
-        room.state = plugin.createInitialState(room.players);
+        room.state = plugin.createInitialState(room.players, room.options);
         room.status = "playing";
         this.scheduleCleanup(roomId, ROOM_CONFIG.PLAYING_MAX_MS);