Fix vertical SegmentedButton not filling available width under bounded constraints (#180701)

Fixes an issue where vertical segments used intrinsic width instead of
expanding to fill the parent's bounded width, resulting in narrow tap
targets.

Fixes [#178901](https://github.com/flutter/flutter/issues/178901)

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above.
- [ ] I updated/added relevant documentation (doc comments with `///`).
- [x] I added new tests to check the change I am making, or this PR is
[test-exempt].
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Fixes] where supported.
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packages/flutter/lib/src/material/segmented_button.dart

diff --git a/packages/flutter/lib/src/material/segmented_button.dart b/packages/flutter/lib/src/material/segmented_button.dart
index 9d6913b..cb056d8 100644
--- a/packages/flutter/lib/src/material/segmented_button.dart
+++ b/packages/flutter/lib/src/material/segmented_button.dart
@@ -998,7 +998,18 @@
       maxWidth = math.max(maxWidth, boxWidth);
       child = childAfter(child);
     }
-    return Size(maxWidth, childHeight);
+
+    var childSize = Size(maxWidth, childHeight);
+
+    // When the parent provides a tight width constraint in the vertical
+    // direction, use that width for layout so the visual size and the
+    // interactive area match. This preserves the intrinsic (shrink-wrap)
+    // sizing behavior when the width is unconstrained.
+    if (constraints.hasTightWidth && childSize.width < constraints.maxWidth) {
+      childSize = Size(constraints.maxWidth, childSize.height);
+    }
+
+    return childSize;
   }
 
   Size _computeOverallSizeFromChildSize(Size childSize) {

packages/flutter/test/material/segmented_button_test.dart

diff --git a/packages/flutter/test/material/segmented_button_test.dart b/packages/flutter/test/material/segmented_button_test.dart
index c1d9250..a49ddf4 100644
--- a/packages/flutter/test/material/segmented_button_test.dart
+++ b/packages/flutter/test/material/segmented_button_test.dart
@@ -1587,6 +1587,52 @@
     );
     expect(tester.getSize(find.byType(SegmentedButton<String>)), Size.zero);
   });
+
+  testWidgets('SegmentedButton should expand to fill the full width', (WidgetTester tester) async {
+    tester.view
+      ..physicalSize = const Size(800, 1200)
+      ..devicePixelRatio = 1.0;
+    addTearDown(tester.view.reset);
+
+    const double screenWidth = 800;
+
+    await tester.pumpWidget(
+      MaterialApp(
+        home: Scaffold(
+          body: Center(
+            child: SizedBox(
+              width: double.infinity,
+              child: SegmentedButton<String>(
+                direction: Axis.vertical,
+                segments: const [
+                  ButtonSegment(value: 'All', label: Text('All')),
+                  ButtonSegment(value: 'Top free', label: Text('Top free')),
+                  ButtonSegment(value: 'Top paid', label: Text('Top paid')),
+                ],
+                selected: const {'All'},
+              ),
+            ),
+          ),
+        ),
+      ),
+    );
+    await tester.pumpAndSettle();
+
+    final RenderBox segmentedBox = tester.renderObject(find.byType(SegmentedButton<String>));
+
+    expect(segmentedBox.size.width, screenWidth);
+
+    final Finder segmentMaterials = find.descendant(
+      of: find.byType(SegmentedButton<String>),
+      matching: find.byType(Material),
+    );
+
+    for (final Element element in segmentMaterials.evaluate()) {
+      final segmentBox = element.renderObject! as RenderBox;
+
+      expect(segmentBox.size.width, screenWidth);
+    }
+  });
 }
 
 Set<WidgetState> enabled = const <WidgetState>{};