Add integration test for Gradle-initiated android builds with flavors (#163737)

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This request is a subset of #157871 and follows up #162907.

#162907 actually fixed behaviour of building with native tooling not
only for iOS/macOS, but also for Android builds too: now on master, if
you start build with `gradle` instead of `flutter build ...` – you also
get the correct behaviour and `appFlavor` won't be null in runtime.
Tests in this PR will check exactly this behavior.

Another diff is the change in the method of obtaining flavor at runtime
inside test project. Before this change, method channels were used for
this, after – `appFlavor` constant. Both methods do more or less the
same thing right now, but they may diverge in future, so I guess this is
the right way to check correctness here. Also, this change was requested
and approved by Andrew in
https://github.com/flutter/flutter/pull/157871#discussion_r1931153339

issue for checklist: #155951 

New test was tested here:
https://ci.chromium.org/ui/p/flutter/builders/try/Linux_pixel_7pro%20flavors_test/63/overview


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dev/integration_tests/flavors/android/app/src/main/java/com/yourcompany/flavors/MainActivity.java

@@ -4,24 +4,6 @@
 
 package com.yourcompany.flavors;
 
-import android.os.Bundle;
-
-import androidx.annotation.NonNull;
 import io.flutter.embedding.android.FlutterActivity;
-import io.flutter.embedding.engine.FlutterEngine;
-import io.flutter.plugin.common.MethodCall;
-import io.flutter.plugin.common.MethodChannel;
-import io.flutter.plugins.GeneratedPluginRegistrant;
 
-public class MainActivity extends FlutterActivity {
-  @Override
-  public void configureFlutterEngine(@NonNull FlutterEngine flutterEngine) {
-    GeneratedPluginRegistrant.registerWith(flutterEngine);
-    new MethodChannel(flutterEngine.getDartExecutor().getBinaryMessenger(), "flavor")
-        .setMethodCallHandler(
-            (call, result) -> {
-                result.success(BuildConfig.FLAVOR);
-        }
-    );
-  }
-}
+public class MainActivity extends FlutterActivity {}

dev/integration_tests/flavors/lib/main.dart

@@ -23,26 +23,11 @@ class Flavor extends StatefulWidget {
 }
 
 class _FlavorState extends State<Flavor> {
-  String? _flavor;
-
-  @override
-  void initState() {
-    super.initState();
-    const MethodChannel('flavor').invokeMethod<String>('getFlavor').then((String? flavor) {
-      setState(() {
-        _flavor = flavor;
-      });
-    });
-  }
-
   @override
   Widget build(BuildContext context) {
-    return Directionality(
+    return const Directionality(
       textDirection: TextDirection.ltr,
-      child:
-          _flavor == null
-              ? const Text('Awaiting flavor...')
-              : Text(_flavor!, key: const ValueKey<String>('flavor')),
+      child: Text(appFlavor ?? 'null', key: ValueKey<String>('flavor')),
     );
   }
 }