fix: use RoomMemoryPairsProvider in room page

Updates /arcade/room/page.tsx to use RoomMemoryPairsProvider instead
of ArcadeMemoryPairsProvider to match the updated component hooks.

The components now use useMemoryPairs() from MemoryPairsContext, which
is provided by RoomMemoryPairsProvider. This fixes the runtime error:
"useMemoryPairs must be used within a MemoryPairsProvider"

Changes:
- Import RoomMemoryPairsProvider instead of ArcadeMemoryPairsProvider
- Wrap matching game with RoomMemoryPairsProvider

Note: ArcadeMemoryPairsProvider can be deprecated in future cleanup.

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

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

apps/web/src/app/arcade/matching/context/index.ts

@@ -0,0 +1,20 @@
+/**
+ * Central export point for arcade matching game context
+ * Re-exports the hook from the appropriate provider
+ */
+
+// Export the hook (works with both local and room providers)
+export { useMemoryPairs } from './MemoryPairsContext'
+
+// Export the room provider (networked multiplayer)
+export { RoomMemoryPairsProvider } from './RoomMemoryPairsProvider'
+
+// Export types
+export type {
+  GameCard,
+  GameMode,
+  GamePhase,
+  GameType,
+  MemoryPairsState,
+  MemoryPairsContextValue,
+} from './types'

apps/web/src/app/arcade/room/page.tsx

@@ -2,7 +2,7 @@
 
 import { useRoomData } from '@/hooks/useRoomData'
 import { MemoryPairsGame } from '../matching/components/MemoryPairsGame'
-import { ArcadeMemoryPairsProvider } from '../matching/context/ArcadeMemoryPairsContext'
+import { RoomMemoryPairsProvider } from '../matching/context/RoomMemoryPairsProvider'
 
 /**
  * /arcade/room - Renders the game for the user's current room
@@ -68,9 +68,9 @@ export default function RoomPage() {
   switch (roomData.gameName) {
     case 'matching':
       return (
-        <ArcadeMemoryPairsProvider>
+        <RoomMemoryPairsProvider>
           <MemoryPairsGame />
-        </ArcadeMemoryPairsProvider>
+        </RoomMemoryPairsProvider>
       )
 
     // TODO: Add other games (complement-race, memory-quiz, etc.)