Repository: flutter
Issue: showDatePicker(): Allowing locale override for InputDatePickerFormField only
Labels: c: new feature,framework,f: material design,f: date/time picker,c: proposal,P3,team-design,triaged-design

### Steps to reproduce

1. Set locale of your app to `Locale('ar')`
2. call `showDatePicker();`
3. The date in the textfield is show arab oriental numbers and not arab numbers.

<img width="499" alt="image" src="https://github.com/flutter/flutter/assets/6270529/4f59099c-608a-4a28-8509-5b47c0e7ae14">


### Expected results

Allowing override local only for TextField.
I want to show "2020/10/10" date for example

### Actual results

The date in the textfield is show arab oriental numbers and not arab numbers.

### Code sample

```dart
await showDatePicker(
        context: context,
        initialDate: selectedDate,
        firstDate: DateTime(2000),
        lastDate: DateTime(2100));
}
  ```

### Screenshots or Video

_No response_

### Logs

_No response_

### Flutter Doctor output

<details open><summary>Doctor output</summary>

```console
[✓] Flutter (Channel stable, 3.22.1, on macOS 14.5 23F79
    darwin-arm64, locale fr-FR)
    • Flutter version 3.22.1 on channel stable at
      /Users/jeromegsq/Documents/Software/flutter
    • Upstream repository https://github.com/flutter/flutter.git
    • Framework revision a14f74ff3a (4 weeks ago), 2024-05-22
      11:08:21 -0500
    • Engine revision 55eae6864b
    • Dart version 3.4.1
    • DevTools version 2.34.3

[✓] Android toolchain - develop for Android devices (Android SDK version 34.0.0)
    • Android SDK at /Users/jeromegsq/Library/Android/sdk
    • Platform android-34, build-tools 34.0.0
    • ANDROID_HOME = /Users/jeromegsq/Library/Android/sdk
    • Java binary at: /Applications/Android Studio.app/Contents/jbr/Contents/Home/bin/java
    • Java version OpenJDK Runtime Environment (build 17.0.9+0-17.0.9b1087.7-11185874)
    • All Android licenses accepted.

[✓] Xcode - develop for iOS and macOS (Xcode 15.0)
    • Xcode at /Applications/Xcode.app/Contents/Developer
    • Build 15A240d
    • CocoaPods version 1.15.2

[✓] Chrome - develop for the web
    • CHROME_EXECUTABLE = /Applications/Google Chrome.app/Contents/MacOS/Google Chrome

[✓] Android Studio (version 2023.2)
    • Android Studio at /Applications/Android Studio.app/Contents
    • Flutter plugin can be installed from:
      🔨 https://plugins.jetbrains.com/plugin/9212-flutter
    • Dart plugin can be installed from:
      🔨 https://plugins.jetbrains.com/plugin/6351-dart
    • Java version OpenJDK Runtime Environment (build 17.0.9+0-17.0.9b1087.7-11185874)

[✓] VS Code (version 1.90.0)
    • VS Code at /Applications/Visual Studio Code.app/Contents
    • Flutter extension version 3.90.0

[✓] Connected device (3 available)
    • macOS (desktop)                 • macos                 • darwin-arm64   • macOS 14.5
      23F79 darwin-arm64
    • Mac Designed for iPad (desktop) • mac-designed-for-ipad • darwin         • macOS 14.5
      23F79 darwin-arm64
    • Chrome (web)                    • chrome                • web-javascript • Google Chrome
      126.0.6478.114
    ! Error: Browsing on the local area network for iPhone de Jerome Ghesquiere. Ensure the
      device is unlocked and attached with a cable or associated with the same local area
      network as this Mac.
      The device must be opted into Developer Mode to connect wirelessly. (code -27)

[✓] Network resources
    • All expected network resources are available.

• No issues found!
```

</details>