[Large screen] Fix searched Subsettings back navigation bug

Settings app registers SubSettings SplitPairRule with clearTop
true, it will finish Settings app if users click back button on
a SubSettings page.

This change registers SubSettings SplitPairRule with clearTop
true when users click a SubSettings item in Settings home menu.

And this change registers SubSettings SplitPairRule with clearTop
false when users click a SubSettings item in search result.

Bug: 204501750
Test: manual
      1. Settings -> Search settings -> search a SubSettings item
         (e.g., Battery)
      2. Click the searched item.
      3. Click back button.
Change-Id: I6e1862de528e971137ae7087de608bbdd79096b2

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

@@ -36,6 +36,7 @@ import androidx.recyclerview.widget.RecyclerView;
 import com.android.settings.R;
 import com.android.settings.SettingsActivity;
 import com.android.settings.Utils;
+import com.android.settings.activityembedding.ActivityEmbeddingRulesController;
 import com.android.settings.activityembedding.ActivityEmbeddingUtils;
 import com.android.settings.core.SubSettingLauncher;
 import com.android.settings.dashboard.DashboardFragment;
@@ -98,6 +99,10 @@ public class TopLevelSettings extends DashboardFragment implements
 
     @Override
     public boolean onPreferenceTreeClick(Preference preference) {
+        // Register SplitPairRule for SubSettings.
+        ActivityEmbeddingRulesController.registerSubSettingsPairRuleIfNeeded(getContext(),
+                true /* clearTop*/);
+
         setHighlightPreferenceKey(preference.getKey());
         return super.onPreferenceTreeClick(preference);
     }