Reland "Remove dual_screen from new_gallery integration test" (#150873)

Relands flutter/flutter#150808

The original version of the pr [accidentally deleted the back button](flutter/flutter#150808 (comment)), which didn't block the app building but made the test hang because it couldn't back out of the demo pages.

Repro-ed the failure, and then tested that 
```
new_gallery_opengles_impeller__transition_perf
new_gallery__transition_perf
new_gallery_impeller_old_zoom__transition_perf
new_gallery__crane_perf
new_gallery_impeller__transition_perf
```

All pass on my pixel 7 pro, with ` dart bin/test_runner.dart test -t <test>`, after re-adding the mistakenly deleted content.

Did not test on an iOS device (I don't have one), but those tests were failing for the same reason from what I can tell:
```
> reply@study
[2024-06-26 12:49:21.884543] [STDOUT] stdout: [        ] scrolling to demo
[2024-06-26 12:49:22.412479] [STDOUT] stdout: [ +527 ms] tapping demo
[2024-06-26 12:49:28.075978] [STDOUT] stderr: [+5663 ms] VMServiceFlutterDriver: tap message is taking a long time to complete...
```
Which is the same error, and which makes sense - they got stuck because they couldn't back out of the page.

Sorry for the churn �

dev/integration_tests/new_gallery/lib/data/demos.dart

@@ -26,8 +26,6 @@ import '../demos/reference/motion_demo_shared_y_axis_transition.dart';
 import '../demos/reference/motion_demo_shared_z_axis_transition.dart';
 import '../demos/reference/transformations_demo.dart'
     deferred as transformations_demo;
-import '../demos/reference/two_pane_demo.dart'
-    deferred as twopane_demo;
 import '../demos/reference/typography_demo.dart'
     deferred as typography;
 import '../gallery_localizations.dart';
@@ -1158,54 +1156,6 @@ class Demos {
 
   static List<GalleryDemo> otherDemos(GalleryLocalizations localizations) {
     return <GalleryDemo>[
-      GalleryDemo(
-        title: localizations.demoTwoPaneTitle,
-        icon: GalleryIcons.bottomSheetPersistent,
-        slug: 'two-pane',
-        subtitle: localizations.demoTwoPaneSubtitle,
-        configurations: <GalleryDemoConfiguration>[
-          GalleryDemoConfiguration(
-            title: localizations.demoTwoPaneFoldableLabel,
-            description: localizations.demoTwoPaneFoldableDescription,
-            documentationUrl:
-                'https://pub.dev/documentation/dual_screen/latest/dual_screen/TwoPane-class.html',
-            buildRoute: (_) => DeferredWidget(
-              twopane_demo.loadLibrary,
-              () => twopane_demo.TwoPaneDemo(
-                type: twopane_demo.TwoPaneDemoType.foldable,
-                restorationId: 'two_pane_foldable',
-              ),
-            ),
-                      ),
-          GalleryDemoConfiguration(
-            title: localizations.demoTwoPaneTabletLabel,
-            description: localizations.demoTwoPaneTabletDescription,
-            documentationUrl:
-                'https://pub.dev/documentation/dual_screen/latest/dual_screen/TwoPane-class.html',
-            buildRoute: (_) => DeferredWidget(
-              twopane_demo.loadLibrary,
-              () => twopane_demo.TwoPaneDemo(
-                type: twopane_demo.TwoPaneDemoType.tablet,
-                restorationId: 'two_pane_tablet',
-              ),
-            ),
-                      ),
-          GalleryDemoConfiguration(
-            title: localizations.demoTwoPaneSmallScreenLabel,
-            description: localizations.demoTwoPaneSmallScreenDescription,
-            documentationUrl:
-                'https://pub.dev/documentation/dual_screen/latest/dual_screen/TwoPane-class.html',
-            buildRoute: (_) => DeferredWidget(
-              twopane_demo.loadLibrary,
-              () => twopane_demo.TwoPaneDemo(
-                type: twopane_demo.TwoPaneDemoType.smallScreen,
-                restorationId: 'two_pane_single',
-              ),
-            ),
-                      ),
-        ],
-        category: GalleryDemoCategory.other,
-      ),
       GalleryDemo(
         title: localizations.demoMotionTitle,
         icon: GalleryIcons.animation,

dev/integration_tests/new_gallery/lib/layout/adaptive.dart

@@ -2,25 +2,20 @@
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
-import 'dart:ui';
-
 import 'package:adaptive_breakpoints/adaptive_breakpoints.dart';
-import 'package:dual_screen/dual_screen.dart';
 import 'package:flutter/material.dart';
 
 /// The maximum width taken up by each item on the home screen.
 const double maxHomeItemWidth = 1400.0;
 
 /// Returns a boolean value whether the window is considered medium or large size.
 ///
-/// When running on a desktop device that is also foldable, the display is not
-/// considered desktop. Widgets using this method might consider the display is
+/// Widgets using this method might consider the display is
 /// large enough for certain layouts, which is not the case on foldable devices,
 /// where only part of the display is available to said widgets.
 ///
 /// Used to build adaptive and responsive layouts.
 bool isDisplayDesktop(BuildContext context) =>
-    !isDisplayFoldable(context) &&
     getWindowType(context) >= AdaptiveWindowType.medium;
 
 /// Returns boolean value whether the window is considered medium size.
@@ -29,16 +24,3 @@ bool isDisplayDesktop(BuildContext context) =>
 bool isDisplaySmallDesktop(BuildContext context) {
   return getWindowType(context) == AdaptiveWindowType.medium;
 }
-
-/// Returns a boolean value whether the display has a hinge that splits the
-/// screen into two, left and right sub-screens. Horizontal splits (top and
-/// bottom sub-screens) are ignored for this application.
-bool isDisplayFoldable(BuildContext context) {
-  final DisplayFeature? hinge = MediaQuery.of(context).hinge;
-  if (hinge == null) {
-    return false;
-  } else {
-    // Vertical
-    return hinge.bounds.size.aspectRatio < 1;
-  }
-}

dev/integration_tests/new_gallery/lib/main.dart

@@ -2,7 +2,6 @@
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
-import 'package:dual_screen/dual_screen.dart';
 import 'package:flutter/foundation.dart';
 import 'package:flutter/material.dart';
 import 'package:flutter/scheduler.dart' show timeDilation;
@@ -50,7 +49,6 @@ class GalleryApp extends StatelessWidget {
       child: Builder(
         builder: (BuildContext context) {
           final GalleryOptions options = GalleryOptions.of(context);
-          final bool hasHinge = MediaQuery.of(context).hinge?.bounds != null;
           return MaterialApp(
             restorationScopeId: 'rootGallery',
             title: 'Flutter Gallery',
@@ -74,7 +72,7 @@ class GalleryApp extends StatelessWidget {
               return basicLocaleListResolution(locales, supportedLocales);
             },
             onGenerateRoute: (RouteSettings settings) =>
-                RouteConfiguration.onGenerateRoute(settings, hasHinge),
+                RouteConfiguration.onGenerateRoute(settings),
           );
         },
       ),