fix(card-sorting): add missing gameMode support after hard reset

After reverting cursor tracking commits, the gameMode type system remained
but implementation was incomplete, causing TypeScript errors. This adds the
missing gameMode handling throughout the codebase.

Changes:
- Add gameMode to createInitialState (Provider and Validator)
- Add gameMode to setConfig type signature and implementation
- Add gameMode validation case in validateSetConfig
- Include gameMode in originalConfig for pause/resume
- Initialize activePlayers, allPlayerMetadata, cursorPositions as empty

Fixes TypeScript errors:
- "Property 'gameMode' is missing" in Provider and Validator
- "Argument of type 'gameMode' not assignable" in SetupPhase

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

apps/web/src/arcade-games/card-sorting/Provider.tsx

@@ -28,7 +28,7 @@ interface CardSortingContextValue {
   revealNumbers: () => void
   goToSetup: () => void
   resumeGame: () => void
-  setConfig: (field: 'cardCount' | 'showNumbers' | 'timeLimit', value: unknown) => void
+  setConfig: (field: 'cardCount' | 'showNumbers' | 'timeLimit' | 'gameMode', value: unknown) => void
   updateCardPositions: (positions: CardPosition[]) => void
   exitSession: () => void
   // Computed
@@ -55,6 +55,7 @@ const createInitialState = (config: Partial<CardSortingConfig>): CardSortingStat
   cardCount: config.cardCount ?? 8,
   showNumbers: config.showNumbers ?? true,
   timeLimit: config.timeLimit ?? null,
+  gameMode: config.gameMode ?? 'solo',
   gamePhase: 'setup',
   playerId: '',
   playerMetadata: {
@@ -63,6 +64,8 @@ const createInitialState = (config: Partial<CardSortingConfig>): CardSortingStat
     emoji: '',
     userId: '',
   },
+  activePlayers: [],
+  allPlayerMetadata: new Map(),
   gameStartTime: null,
   gameEndTime: null,
   selectedCards: [],
@@ -70,6 +73,7 @@ const createInitialState = (config: Partial<CardSortingConfig>): CardSortingStat
   availableCards: [],
   placedCards: new Array(config.cardCount ?? 8).fill(null),
   cardPositions: [],
+  cursorPositions: new Map(),
   selectedCardId: null,
   numbersRevealed: false,
   scoreBreakdown: null,
@@ -91,6 +95,8 @@ function applyMoveOptimistically(state: CardSortingState, move: GameMove): CardS
         gamePhase: 'playing',
         playerId: typedMove.playerId,
         playerMetadata: typedMove.data.playerMetadata,
+        activePlayers: [typedMove.playerId],
+        allPlayerMetadata: new Map([[typedMove.playerId, typedMove.data.playerMetadata]]),
         gameStartTime: Date.now(),
         selectedCards,
         correctOrder,
@@ -103,6 +109,7 @@ function applyMoveOptimistically(state: CardSortingState, move: GameMove): CardS
           cardCount: state.cardCount,
           showNumbers: state.showNumbers,
           timeLimit: state.timeLimit,
+          gameMode: state.gameMode,
         },
         pausedGamePhase: undefined,
         pausedGameState: undefined,
@@ -535,7 +542,7 @@ export function CardSortingProvider({ children }: { children: ReactNode }) {
   }, [localPlayerId, canResumeGame, sendMove, viewerId])
 
   const setConfig = useCallback(
-    (field: 'cardCount' | 'showNumbers' | 'timeLimit', value: unknown) => {
+    (field: 'cardCount' | 'showNumbers' | 'timeLimit' | 'gameMode', value: unknown) => {
       if (!localPlayerId) return
 
       sendMove({

apps/web/src/arcade-games/card-sorting/Validator.ts

@@ -323,11 +323,13 @@ export class CardSortingValidator implements GameValidator<CardSortingState, Car
             cardCount: state.cardCount,
             showNumbers: state.showNumbers,
             timeLimit: state.timeLimit,
+            gameMode: state.gameMode,
           }),
           originalConfig: {
             cardCount: state.cardCount,
             showNumbers: state.showNumbers,
             timeLimit: state.timeLimit,
+            gameMode: state.gameMode,
           },
           pausedGamePhase: 'playing',
           pausedGameState: {
@@ -349,6 +351,7 @@ export class CardSortingValidator implements GameValidator<CardSortingState, Car
         cardCount: state.cardCount,
         showNumbers: state.showNumbers,
         timeLimit: state.timeLimit,
+        gameMode: state.gameMode,
       }),
     }
   }
@@ -414,6 +417,24 @@ export class CardSortingValidator implements GameValidator<CardSortingState, Car
           },
         }
 
+      case 'gameMode':
+        if (!['solo', 'collaborative', 'competitive', 'relay'].includes(value as string)) {
+          return {
+            valid: false,
+            error: 'gameMode must be solo, collaborative, competitive, or relay',
+          }
+        }
+        return {
+          valid: true,
+          newState: {
+            ...state,
+            gameMode: value as 'solo' | 'collaborative' | 'competitive' | 'relay',
+            // Clear pause state if config changed
+            pausedGamePhase: undefined,
+            pausedGameState: undefined,
+          },
+        }
+
       default:
         return { valid: false, error: `Unknown config field: ${field}` }
     }
@@ -500,6 +521,7 @@ export class CardSortingValidator implements GameValidator<CardSortingState, Car
       cardCount: config.cardCount,
       showNumbers: config.showNumbers,
       timeLimit: config.timeLimit,
+      gameMode: config.gameMode,
       gamePhase: 'setup',
       playerId: '',
       playerMetadata: {
@@ -508,6 +530,8 @@ export class CardSortingValidator implements GameValidator<CardSortingState, Car
         emoji: '',
         userId: '',
       },
+      activePlayers: [],
+      allPlayerMetadata: new Map(),
       gameStartTime: null,
       gameEndTime: null,
       selectedCards: [],
@@ -515,6 +539,7 @@ export class CardSortingValidator implements GameValidator<CardSortingState, Car
       availableCards: [],
       placedCards: new Array(config.cardCount).fill(null),
       cardPositions: [],
+      cursorPositions: new Map(),
       selectedCardId: null,
       numbersRevealed: false,
       scoreBreakdown: null,