Fix wide DatePicker input mode button padding for Material 3 (#147236)

fixes [Wide `DatePickerDialog` "Switch to input" button has no margin from dialog side](#141338)

### Description
Currently, there is no material design token for the input mode button padding. This PR fixes the padding by taking date picker side padding values into account.

![specs](https://github.com/flutter/flutter/assets/48603081/4d946d57-1e00-4b11-b414-0788a20fe0cb)

### Code sample

<details>
<summary>expand to view the code sample</summary> 

```dart
import 'package:flutter/material.dart';

void main() {
  runApp(const MyApp());
}

class MyApp extends StatelessWidget {
  const MyApp({super.key});

  @OverRide
  Widget build(BuildContext context) {
    return MaterialApp(
      home: Scaffold(
        body: Center(
          child: Builder(builder: (BuildContext context) {
            return ElevatedButton(
              onPressed: () {
                showDatePicker(
                  context: context,
                  initialDate: DateTime.now(),
                  firstDate: DateTime.utc(2010),
                  lastDate: DateTime.utc(2030),
                );
              },
              child: const Text('Show Date Picker'),
            );
          }),
        ),
      ),
    );
  }
}

```

</details>

### Before
![before](https://github.com/flutter/flutter/assets/48603081/e3a70179-540f-4307-b996-7cf35d28adbc)

### After
![after](https://github.com/flutter/flutter/assets/48603081/c65a2d1d-b0ae-4969-868e-e64f5c845fcb)

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

@@ -837,11 +837,12 @@ class _DatePickerHeader extends StatelessWidget {
 
   @override
   Widget build(BuildContext context) {
-    final DatePickerThemeData themeData = DatePickerTheme.of(context);
+    final ThemeData theme = Theme.of(context);
+    final DatePickerThemeData datePickerTheme = DatePickerTheme.of(context);
     final DatePickerThemeData defaults = DatePickerTheme.defaults(context);
-    final Color? backgroundColor = themeData.headerBackgroundColor ?? defaults.headerBackgroundColor;
-    final Color? foregroundColor = themeData.headerForegroundColor ?? defaults.headerForegroundColor;
-    final TextStyle? helpStyle = (themeData.headerHelpStyle ?? defaults.headerHelpStyle)?.copyWith(
+    final Color? backgroundColor = datePickerTheme.headerBackgroundColor ?? defaults.headerBackgroundColor;
+    final Color? foregroundColor = datePickerTheme.headerForegroundColor ?? defaults.headerForegroundColor;
+    final TextStyle? helpStyle = (datePickerTheme.headerHelpStyle ?? defaults.headerHelpStyle)?.copyWith(
       color: foregroundColor,
     );
 
@@ -923,7 +924,16 @@ class _DatePickerHeader extends StatelessWidget {
                   ),
                   if (entryModeButton != null)
                     Padding(
-                      padding: const EdgeInsets.symmetric(horizontal: 4),
+                      padding: theme.useMaterial3
+                        // TODO(TahaTesser): This is an eye-balled M3 entry mode button padding
+                        // from https://m3.material.io/components/date-pickers/specs#c16c142b-4706-47f3-9400-3cde654b9aa8.
+                        // Update this value to use tokens when available.
+                        ? const EdgeInsetsDirectional.only(
+                            start: 8.0,
+                            end: 4.0,
+                            bottom: 6.0,
+                          )
+                        : const EdgeInsets.symmetric(horizontal: 4),
                       child: Semantics(
                         container: true,
                         child: entryModeButton,

packages/flutter/test/material/date_picker_test.dart

@@ -871,9 +871,13 @@ void main() {
       // Test switch button position.
       final Finder switchButtonM3 = find.widgetWithIcon(IconButton, Icons.edit_outlined);
       final Offset switchButtonTopLeft = tester.getTopLeft(switchButtonM3);
+      final Offset switchButtonBottomLeft = tester.getBottomLeft(switchButtonM3);
       final Offset headerTextBottomLeft = tester.getBottomLeft(headerText);
-      expect(switchButtonTopLeft.dx, dialogTopLeft.dx + 4.0);
+      final Offset dialogBottomLeft = tester.getBottomLeft(find.byType(AnimatedContainer));
+      expect(switchButtonTopLeft.dx, dialogTopLeft.dx + 8.0);
       expect(switchButtonTopLeft.dy, headerTextBottomLeft.dy);
+      expect(switchButtonBottomLeft.dx, dialogTopLeft.dx + 8.0);
+      expect(switchButtonBottomLeft.dy, dialogBottomLeft.dy - 6.0);
 
       // Test vertical divider position.
       final Finder divider = find.byType(VerticalDivider);