App close auto shred not working [Tablet] (#34702)

Fixed the `On App Closed` auto-shred option to trigger only when the app
is fully closed, not when the user switches apps or presses the Home
button.

Resolves: https://github.com/brave/brave-browser/issues/53441
---------

Signed-off-by: Vadym Struts <vstruts@brave.com>

android/java/org/chromium/chrome/browser/app/BraveActivity.java

@@ -1098,12 +1098,6 @@ public abstract class BraveActivity extends ChromeActivity
             ApplicationStatus.registerApplicationStateListener(mApplicationStateListener);
         }
 
-        Profile profile = getCurrentProfile();
-        if (profile != null) {
-            // Triggers notification of current app state on Android.
-            BraveFirstPartyStorageCleanerUtils.triggerCurrentAppStateNotification(profile);
-        }
-
         super.onStartWithNative();
     }
 
@@ -3031,4 +3025,14 @@ public abstract class BraveActivity extends ChromeActivity
             }
         }
     }
+
+    @Override
+    public void onTabStateInitializedHandler() {
+        Profile profile = getCurrentProfile();
+        if (profile != null) {
+            // Triggers current app state notification to make sure the first-party storage cleanup
+            // is scheduled on startup if needed.
+            BraveFirstPartyStorageCleanerUtils.triggerCurrentAppStateNotification(profile);
+        }
+    }
 }