Update MaterialScrollBehavior.buildScrollbar for horizontal axes (#87740)

packages/flutter/lib/src/material/app.dart

@@ -693,8 +693,13 @@ class MaterialApp extends StatefulWidget {
 /// [GlowingOverscrollIndicator] to [Scrollable] descendants when executing on
 /// [TargetPlatform.android] and [TargetPlatform.fuchsia].
 ///
-/// When using the desktop platform, if the [Scrollable] widget scrolls in the
-/// [Axis.vertical], a [Scrollbar] is applied.
+/// The [buildScrollbar] function is called by the [Scrollable] to wrap with a
+/// [Scrollbar] when appropriate. On all platforms, when the Scrollable [Axis] is
+/// [Axis.horizontal], an always visible Scrollbar will be applied. This is
+/// because horizontal [ScrollView]s have lower discoverability as scrollable
+/// content. When the Axis is [Axis.vertical] a Scrollbar is applied on
+/// desktop platforms. In this vertical case, [Scrollbar.isAlwaysShown] is not
+/// set and will defer to the inherited [ScrollbarTheme].
 ///
 /// See also:
 ///
@@ -716,7 +721,11 @@ class MaterialScrollBehavior extends ScrollBehavior {
     // the base class as well.
     switch (axisDirectionToAxis(details.direction)) {
       case Axis.horizontal:
-        return child;
+        return Scrollbar(
+          isAlwaysShown: true,
+          controller: details.controller,
+          child: child,
+        );
       case Axis.vertical:
         switch (getPlatform(context)) {
           case TargetPlatform.linux:

packages/flutter/lib/src/material/tabs.dart

@@ -1308,13 +1308,16 @@ class _TabBarState extends State<TabBar> {
 
     if (widget.isScrollable) {
       _scrollController ??= _TabBarScrollController(this);
-      tabBar = SingleChildScrollView(
-        dragStartBehavior: widget.dragStartBehavior,
-        scrollDirection: Axis.horizontal,
-        controller: _scrollController,
-        padding: widget.padding,
-        physics: widget.physics,
-        child: tabBar,
+      tabBar = ScrollConfiguration(
+        behavior: ScrollConfiguration.of(context).copyWith(scrollbars: false),
+        child: SingleChildScrollView(
+          dragStartBehavior: widget.dragStartBehavior,
+          scrollDirection: Axis.horizontal,
+          controller: _scrollController,
+          padding: widget.padding,
+          physics: widget.physics,
+          child: tabBar,
+        ),
       );
     } else if (widget.padding != null) {
       tabBar = Padding(

packages/flutter/test/material/scrollbar_test.dart

@@ -1557,4 +1557,20 @@ void main() {
         ),
     );
   });
+
+  testWidgets('MaterialScrollBehavior applies always shown Scrollbar to horizontal scrollables', (WidgetTester tester) async {
+    final ScrollController controller = ScrollController();
+    await tester.pumpWidget(MaterialApp(
+      home: SingleChildScrollView(
+        scrollDirection: Axis.horizontal,
+        controller: controller,
+        child: const SizedBox(
+          width: 4000.0,
+          height: 4000.0,
+        ),
+      ),
+    ));
+    await tester.pumpAndSettle();
+    expect(find.byType(Scrollbar), paints..rect());
+  });
 }