Launch new Home app when selecting Home app in Settings

Launches the newly selected Home app when it has been selected in
Default Home app settings. This CL makes the change take effect
immediately, instead of when the Home button is pressed.

Bug: 70697830
Test: make RunSettingsRoboTests
Test: Manual - Change default home app in Settings
Change-Id: If7e2956bc6f8ddba0a7e8da48a0d38e3936c57e9

tests/robotests/src/com/android/settings/applications/defaultapps/DefaultHomePickerTest.java

@@ -73,6 +73,7 @@ public class DefaultHomePickerTest {
     @Mock
     private PackageManager mPackageManager;
 
+    private Context mContext;
     private DefaultHomePicker mPicker;
 
     @Before
@@ -85,7 +86,8 @@ public class DefaultHomePickerTest {
         mPicker.onAttach((Context) mActivity);
 
         ReflectionHelpers.setField(mPicker, "mPm", mPackageManagerWrapper);
-        doReturn(RuntimeEnvironment.application).when(mPicker).getContext();
+        mContext = spy(RuntimeEnvironment.application);
+        doReturn(mContext).when(mPicker).getContext();
     }
 
     @Test
@@ -94,6 +96,7 @@ public class DefaultHomePickerTest {
 
         verify(mPackageManagerWrapper).replacePreferredActivity(any(IntentFilter.class),
                 anyInt(), any(ComponentName[].class), any(ComponentName.class));
+        verify(mContext).startActivity(any());
     }
 
     @Test