fix(arcade): prevent gameConfig from being overwritten when switching games

Root cause: setRoomGameApi was sending `gameConfig: {}` when gameConfig
was undefined, which overwrote all saved settings in the database.

Changes:
- Client: Only include gameConfig in request body if explicitly provided
- Server: Only include gameConfig in socket broadcast if provided
- Client handler: Update gameConfig from broadcast if present

This preserves all game settings (difficulty, card count, etc.) when
switching between games in a room.

🤖 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

@@ -117,11 +117,21 @@ export async function PATCH(req: NextRequest, context: RouteContext) {
       if (io) {
         try {
           console.log(`[Settings API] Broadcasting game change to room ${roomId}: ${body.gameName}`)
-          io.to(`room:${roomId}`).emit('room-game-changed', {
+          const broadcastData: {
+            roomId: string
+            gameName: string | null
+            gameConfig?: Record<string, unknown>
+          } = {
             roomId,
             gameName: body.gameName,
-            gameConfig: body.gameConfig || {},
-          })
+          }
+
+          // Only include gameConfig if it was explicitly provided
+          if (body.gameConfig !== undefined) {
+            broadcastData.gameConfig = body.gameConfig
+          }
+
+          io.to(`room:${roomId}`).emit('room-game-changed', broadcastData)
         } catch (socketError) {
           console.error('[Settings API] Failed to broadcast game change:', socketError)
         }

apps/web/src/hooks/useRoomData.ts

@@ -449,7 +449,7 @@ export function useRoomData() {
     const handleRoomGameChanged = (data: {
       roomId: string
       gameName: string | null
-      gameConfig: Record<string, unknown>
+      gameConfig?: Record<string, unknown>
     }) => {
       console.log('[useRoomData] Room game changed:', data)
       if (data.roomId === roomData?.id) {
@@ -458,6 +458,8 @@ export function useRoomData() {
           return {
             ...prev,
             gameName: data.gameName,
+            // Only update gameConfig if it was provided in the broadcast
+            ...(data.gameConfig !== undefined ? { gameConfig: data.gameConfig } : {}),
           }
         })
       }
@@ -585,13 +587,20 @@ async function setRoomGameApi(params: {
   gameName: string
   gameConfig?: Record<string, unknown>
 }): Promise<void> {
+  // Only include gameConfig in the request if it was explicitly provided
+  // Otherwise, we preserve the existing gameConfig in the database
+  const body: { gameName: string; gameConfig?: Record<string, unknown> } = {
+    gameName: params.gameName,
+  }
+
+  if (params.gameConfig !== undefined) {
+    body.gameConfig = params.gameConfig
+  }
+
   const response = await fetch(`/api/arcade/rooms/${params.roomId}/settings`, {
     method: 'PATCH',
     headers: { 'Content-Type': 'application/json' },
-    body: JSON.stringify({
-      gameName: params.gameName,
-      gameConfig: params.gameConfig || {},
-    }),
+    body: JSON.stringify(body),
   })
 
   if (!response.ok) {