chore: App.vue and useGameEngine updates

src/App.vue

@@ -1,5 +1,5 @@
 <script setup lang="ts">
-import { ref, watch, onMounted, onUnmounted } from 'vue'
+import { ref, watch, onMounted, onUnmounted, nextTick } from 'vue'
 import GamePlayer from '@/components/GamePlayer.vue'
 import ChoicePanel from '@/components/ChoicePanel.vue'
 import QTEOverlay from '@/components/QTEOverlay.vue'
@@ -84,6 +84,7 @@ async function init() {
     const params = new URLSearchParams(location.search)
     if (params.get('startScene')) {
       showIntro.value = false
+      await nextTick()
       handleStartFromScene(params.get('startScene')!)
       return
     }
@@ -92,6 +93,7 @@ async function init() {
     const params = new URLSearchParams(location.search)
     const startSceneId = params.get('startScene')
     if (startSceneId) {
+      await nextTick()
       handleStartFromScene(startSceneId)
     }
   }