feat(game): add GameWritebackEventDto and update related services for game state management

.idea/gradle.xml

@@ -5,7 +5,7 @@
     <option name="linkedExternalProjectsSettings">
       <GradleProjectSettings>
         <option name="externalProjectPath" value="$PROJECT_DIR$" />
-        <option name="gradleJvm" value="corretto-21" />
+        <option name="gradleJvm" value="ms-21" />
         <option name="modules">
           <set>
             <option value="$PROJECT_DIR$" />

.idea/misc.xml

@@ -1,9 +1,10 @@
+<?xml version="1.0" encoding="UTF-8"?>
 <project version="4">
   <component name="ExternalStorageConfigurationManager" enabled="true" />
   <component name="FrameworkDetectionExcludesConfiguration">
     <file type="web" url="file://$PROJECT_DIR$" />
   </component>
-  <component name="ProjectRootManager" version="2" languageLevel="JDK_21" default="true" project-jdk-name="corretto-21" project-jdk-type="JavaSDK">
+  <component name="ProjectRootManager" version="2" languageLevel="JDK_21" default="true" project-jdk-name="ms-21" project-jdk-type="JavaSDK">
     <output url="file://$PROJECT_DIR$/out" />
   </component>
 </project>