feat(memory-quiz): persist game settings per-game across sessions

Implement per-game settings persistence so that when users switch between
games and come back, their settings are restored. Settings are saved to
the room's gameConfig field in the database.

Changes:
- Add useUpdateGameConfig hook to save settings to room
- Load settings from roomData.gameConfig on provider initialization
- Merge saved config with initialState using useMemo
- Save settings to database when setConfig is called
- Settings persist across:
  - Game switches (memory-quiz -> matching -> memory-quiz)
  - Page refreshes
  - New arcade sessions

Settings saved: selectedCount, displayTime, selectedDifficulty, playMode

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

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

apps/web/src/app/arcade/memory-quiz/context/RoomMemoryQuizProvider.tsx

@@ -1,10 +1,10 @@
 'use client'
 
 import type { ReactNode } from 'react'
-import { useCallback, useEffect, useState } from 'react'
+import { useCallback, useEffect, useMemo, useState } from 'react'
 import { useGameMode } from '@/contexts/GameModeContext'
 import { useArcadeSession } from '@/hooks/useArcadeSession'
-import { useRoomData } from '@/hooks/useRoomData'
+import { useRoomData, useUpdateGameConfig } from '@/hooks/useRoomData'
 import { useViewerId } from '@/hooks/useViewerId'
 import type { GameMove } from '@/lib/arcade/validation'
 import { TEAM_MOVE } from '@/lib/arcade/validation/types'
@@ -238,6 +238,7 @@ export function RoomMemoryQuizProvider({ children }: { children: ReactNode }) {
   const { data: viewerId } = useViewerId()
   const { roomData } = useRoomData()
   const { activePlayers: activePlayerIds, players } = useGameMode()
+  const { mutate: updateGameConfig } = useUpdateGameConfig()
 
   // Get active player IDs as array
   const activePlayers = Array.from(activePlayerIds)
@@ -246,6 +247,23 @@ export function RoomMemoryQuizProvider({ children }: { children: ReactNode }) {
   // This prevents sending a network request for every keystroke
   const [localCurrentInput, setLocalCurrentInput] = useState('')
 
+  // Merge saved game config from room with initialState
+  const mergedInitialState = useMemo(() => {
+    const savedConfig = roomData?.gameConfig as Record<string, any> | null | undefined
+    if (!savedConfig) return initialState
+
+    console.log('[RoomMemoryQuizProvider] Loading saved game config:', savedConfig)
+
+    return {
+      ...initialState,
+      // Restore settings from saved config
+      selectedCount: savedConfig.selectedCount ?? initialState.selectedCount,
+      displayTime: savedConfig.displayTime ?? initialState.displayTime,
+      selectedDifficulty: savedConfig.selectedDifficulty ?? initialState.selectedDifficulty,
+      playMode: savedConfig.playMode ?? initialState.playMode,
+    }
+  }, [roomData?.gameConfig])
+
   // Arcade session integration WITH room sync
   const {
     state,
@@ -255,7 +273,7 @@ export function RoomMemoryQuizProvider({ children }: { children: ReactNode }) {
   } = useArcadeSession<SorobanQuizState>({
     userId: viewerId || '',
     roomId: roomData?.id, // CRITICAL: Pass roomId for network sync across room members
-    initialState,
+    initialState: mergedInitialState,
     applyMove: applyMoveOptimistically,
   })
 
@@ -421,8 +439,21 @@ export function RoomMemoryQuizProvider({ children }: { children: ReactNode }) {
         userId: viewerId || '',
         data: { field, value },
       })
+
+      // Save setting to room's gameConfig for persistence
+      if (roomData?.id) {
+        const updatedConfig = {
+          ...(roomData.gameConfig as Record<string, any>),
+          [field]: value,
+        }
+        console.log('[RoomMemoryQuizProvider] Saving game config:', updatedConfig)
+        updateGameConfig({
+          roomId: roomData.id,
+          gameConfig: updatedConfig,
+        })
+      }
     },
-    [viewerId, sendMove]
+    [viewerId, sendMove, roomData?.id, roomData?.gameConfig, updateGameConfig]
   )
 
   // Merge network state with local input state

apps/web/src/hooks/useRoomData.ts

@@ -665,3 +665,34 @@ export function useClearRoomGame() {
     },
   })
 }
+
+/**
+ * Update game config for current room (game-specific settings)
+ */
+async function updateGameConfigApi(params: {
+  roomId: string
+  gameConfig: Record<string, unknown>
+}): Promise<void> {
+  const response = await fetch(`/api/arcade/rooms/${params.roomId}/settings`, {
+    method: 'PATCH',
+    headers: { 'Content-Type': 'application/json' },
+    body: JSON.stringify({
+      gameConfig: params.gameConfig,
+    }),
+  })
+
+  if (!response.ok) {
+    const errorData = await response.json()
+    throw new Error(errorData.error || 'Failed to update game config')
+  }
+}
+
+/**
+ * Hook: Update game config for current room
+ * This allows games to persist their settings (e.g., difficulty, card count)
+ */
+export function useUpdateGameConfig() {
+  return useMutation({
+    mutationFn: updateGameConfigApi,
+  })
+}