fix(arcade): delete old session when room game changes

When changing a room's game via the settings API, the old arcade
session was persisting with the previous game's state. This caused
users to still see the old game after selecting a new one.

Changes:
- Delete existing arcade session when gameName is updated in room settings
- Add debug logging to room page game selection handler
- Ensure fresh session is created with new game settings

This fixes the issue where clicking Memory Lightning would not
properly switch the game from Battle Arena.

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

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

apps/web/src/app/api/arcade/rooms/[roomId]/settings/route.ts

@@ -97,6 +97,13 @@ export async function PATCH(req: NextRequest, context: RouteContext) {
       updateData.gameConfig = body.gameConfig
     }
 
+    // If game is being changed (or cleared), delete the existing arcade session
+    // This ensures a fresh session will be created with the new game settings
+    if (body.gameName !== undefined) {
+      console.log(`[Settings API] Deleting existing arcade session for room ${roomId}`)
+      await db.delete(schema.arcadeSessions).where(eq(schema.arcadeSessions.roomId, roomId))
+    }
+
     // Update room settings
     const [updatedRoom] = await db
       .update(schema.arcadeRooms)

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

@@ -87,13 +87,32 @@ export default function RoomPage() {
   // Show game selection if no game is set
   if (!roomData.gameName) {
     const handleGameSelect = (gameType: GameType) => {
+      console.log('[RoomPage] handleGameSelect called with gameType:', gameType)
+
       const gameConfig = GAMES_CONFIG[gameType]
+      console.log('[RoomPage] Game config:', {
+        name: gameConfig.name,
+        available: gameConfig.available,
+      })
+
       if (gameConfig.available === false) {
+        console.log('[RoomPage] Game not available, blocking selection')
         return // Don't allow selecting unavailable games
       }
 
       // Map GameType to internal game name
       const internalGameName = GAME_TYPE_TO_NAME[gameType]
+      console.log('[RoomPage] Mapping:', {
+        gameType,
+        internalGameName,
+        mappingExists: !!internalGameName,
+      })
+
+      console.log('[RoomPage] Calling setRoomGame with:', {
+        roomId: roomData.id,
+        gameName: internalGameName,
+        gameConfig: {},
+      })
 
       setRoomGame({
         roomId: roomData.id,