GameManager: Add Public API

Add the public API to GameManager:
- getGameMode()

Bug: b/178860939
Test: atest CtsGameManagerTestCases
Test: atest GameManagerTests
Test: atest GameManagerServiceTests
Test: atest GameManagerServiceSettingsTests
Change-Id: Ie6030e4ec796c9ecf2c756f24f00e445572accda
diff --git a/packages/Shell/AndroidManifest.xml b/packages/Shell/AndroidManifest.xml
index 1393116..0687191 100644
--- a/packages/Shell/AndroidManifest.xml
+++ b/packages/Shell/AndroidManifest.xml
@@ -418,6 +418,9 @@
     <!-- Permission required for CTS test - PeopleManagerTest -->
     <uses-permission android:name="android.permission.READ_PEOPLE_DATA" />
 
+    <!-- Permission required for CTS test - CtsGameManagerTestCases -->
+    <uses-permission android:name="android.permission.MANAGE_GAME_MODE" />
+
     <application android:label="@string/app_label"
                 android:theme="@android:style/Theme.DeviceDefault.DayNight"
                 android:defaultToDeviceProtectedStorage="true"