Fix unexpected shown of Scrollbar (#159386)

Fixes [Narrow DatePickerDialog has unnecessary scrollbar on months with
6 rows #141348](https://github.com/flutter/flutter/issues/141348)

## Details

`288 / 7 + 288 / 7 * 6 = 288.00000000000006`

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- [x] I listed at least one issue that this PR fixes in the description
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/widgets/scrollbar.dart

@@ -517,9 +517,7 @@ class ScrollbarPainter extends ChangeNotifier implements CustomPainter {
     _lastMetrics = metrics;
     _lastAxisDirection = axisDirection;
 
-    bool needPaint(ScrollMetrics? metrics) =>
-        metrics != null && metrics.maxScrollExtent > metrics.minScrollExtent;
-    if (!needPaint(oldMetrics) && !needPaint(metrics)) {
+    if (!_needPaint(oldMetrics) && !_needPaint(metrics)) {
       return;
     }
     notifyListeners();
@@ -537,6 +535,11 @@ class ScrollbarPainter extends ChangeNotifier implements CustomPainter {
     return Paint()..color = color.withOpacity(color.opacity * fadeoutOpacityAnimation.value);
   }
 
+  bool _needPaint(ScrollMetrics? metrics) {
+    return metrics != null &&
+        metrics.maxScrollExtent - metrics.minScrollExtent > precisionErrorTolerance;
+  }
+
   Paint _paintTrack({bool isBorder = false}) {
     if (isBorder) {
       return Paint()
@@ -629,9 +632,7 @@ class ScrollbarPainter extends ChangeNotifier implements CustomPainter {
 
   @override
   void paint(Canvas canvas, Size size) {
-    if (_lastAxisDirection == null ||
-        _lastMetrics == null ||
-        _lastMetrics!.maxScrollExtent <= _lastMetrics!.minScrollExtent) {
+    if (_lastAxisDirection == null || !_needPaint(_lastMetrics)) {
       return;
     }
     // Skip painting if there's not enough space.

packages/flutter/test/widgets/scrollbar_test.dart

@@ -5,8 +5,8 @@
 import 'dart:ui' as ui;
 
 import 'package:flutter/foundation.dart';
+import 'package:flutter/material.dart';
 import 'package:flutter/src/physics/utils.dart' show nearEqual;
-import 'package:flutter/widgets.dart';
 import 'package:flutter_test/flutter_test.dart';
 
 const Color _kScrollbarColor = Color(0xFF123456);
@@ -3484,4 +3484,46 @@ The provided ScrollController cannot be shared by multiple ScrollView widgets.''
     expect(verticalScrollController.offset, greaterThan(0.0));
     expect(horizontalScrollController.offset, greaterThan(0.0));
   });
+
+  // Regression test for https://github.com/flutter/flutter/issues/141348.
+  testWidgets(
+    'Scrollbar should not shown due to precision error on desktop',
+    (WidgetTester tester) async {
+      Widget buildFrame(Size size) {
+        tester.view.physicalSize = size;
+        tester.view.devicePixelRatio = 1.0;
+        addTearDown(tester.view.reset);
+        return MaterialApp(
+          home: Scaffold(
+            body: Center(
+              child: DatePickerDialog(
+                initialDate: DateTime(2020, DateTime.may), // Month with six rows.
+                firstDate: DateTime(2010),
+                lastDate: DateTime(2030),
+              ),
+            ),
+          ),
+        );
+      }
+
+      const Size screenSizePortrait = Size(400, 600);
+      await tester.pumpWidget(buildFrame(screenSizePortrait));
+      await tester.pumpAndSettle();
+
+      // Scrollbar is not shown.
+      expect(find.byType(Scrollbar), findsOneWidget);
+      expect(find.byType(Scrollbar), isNot(paints..rect()));
+
+      // Scroll on the Scrollbar.
+      final TestPointer pointer = TestPointer(1, ui.PointerDeviceKind.mouse);
+      pointer.hover(tester.getCenter(find.byType(Scrollbar)));
+      await tester.sendEventToBinding(pointer.scroll(const Offset(0.0, 10.0)));
+      await tester.pumpAndSettle();
+
+      // Scrollbar is still not shown.
+      expect(find.byType(Scrollbar), findsOneWidget);
+      expect(find.byType(Scrollbar), isNot(paints..rect()));
+    },
+    variant: TargetPlatformVariant.desktop(),
+  );
 }