[Activity embedding] Fix unexpected finished 2nd layer problem

If Settings is started on an existing task, the existing SplitPairRule
may cause an unexpected app finish while navigating back from the
2nd layer page.

This change resets SplitPairRule in onCreate().

Bug: 247080168
Test: make RunSettingsRoboTests ROBOTEST_FILTER=SettingsHomepageActivityTest
      manual
      1. Settings app -> 'Connexted device'.
      2. Launch Settings app again from Settings icon in quick Settings.
      3. Start a 3rd layer from 'Network & internet'
      4. Click back and see if the 2nd lay shows.
Change-Id: I262327cc49c3a4434a183eb00ac57f47fa598f70

src/com/android/settings/homepage/SettingsHomepageActivity.java

@@ -43,6 +43,7 @@ import android.widget.FrameLayout;
 import android.widget.ImageView;
 import android.widget.Toolbar;
 
+import androidx.annotation.VisibleForTesting;
 import androidx.core.graphics.Insets;
 import androidx.core.view.ViewCompat;
 import androidx.core.view.WindowCompat;
@@ -223,10 +224,23 @@ public class SettingsHomepageActivity extends FragmentActivity implements
         if (shouldLaunchDeepLinkIntentToRight()) {
             launchDeepLinkIntentToRight();
         }
+
+        // Settings app may be launched on an existing task. Reset SplitPairRule of SubSettings here
+        // to prevent SplitPairRule of an existing task applied on a new started Settings app.
+        if (ActivityEmbeddingUtils.isEmbeddingActivityEnabled(this)
+                && (getIntent().getFlags() & Intent.FLAG_ACTIVITY_CLEAR_TOP) != 0) {
+            initSplitPairRules();
+        }
+
         updateHomepagePaddings();
         updateSplitLayout();
     }
 
+    @VisibleForTesting
+    void initSplitPairRules() {
+        new ActivityEmbeddingRulesController(getApplicationContext()).initRules();
+    }
+
     @Override
     protected void onStart() {
         ((SettingsApplication) getApplication()).setHomeActivity(this);