Repository: flutter
Issue: button locale does not populate to the opened sign in page
Labels: a: internationalization,platform-web,p: google_sign_in,package,has reproducible steps,P2,team-web,triaged-web,found in release: 3.13,found in release: 3.14

### Is there an existing issue for this?

- [X] I have searched the [existing issues](https://github.com/flutter/flutter/issues)
- [X] I have read the [guide to filing a bug](https://flutter.dev/docs/resources/bug-reports)

### Steps to reproduce

1. simple login button
```
Widget buildSignInButton({HandleSignInFn? onPressed, required String locale}) {
  return (GoogleSignInPlatform.instance as web.GoogleSignInPlugin).renderButton(
      configuration: GSIButtonConfiguration(
    locale: locale,
  ));
}
```

2. with `fr` value, renders nicely the button in french
![image](https://github.com/flutter/flutter/assets/38670061/9d14803a-bc5e-40db-a497-2cdf9b69cfca)

3. but the login flow renders the next pop up window in english
![image](https://github.com/flutter/flutter/assets/38670061/600da54f-b6cc-4392-9e9a-07cbda4b9578)

4. maybe just need to append `&hl=fr-CA` ? or maybe anything else?
not sure

Please and Thank You :)


### Expected results

french
![image](https://github.com/flutter/flutter/assets/38670061/b82be209-8be9-44aa-b511-dbb86e783a27)


### Actual results

english
![image](https://github.com/flutter/flutter/assets/38670061/192573fe-6d25-4b2c-bdbd-3584cc167aea)


### Code sample

<details><summary>Code sample</summary>

```
Widget buildSignInButton({HandleSignInFn? onPressed, required String locale}) {
  return (GoogleSignInPlatform.instance as web.GoogleSignInPlugin).renderButton(
      configuration: GSIButtonConfiguration(
    locale: locale,
  ));
}
```

</details>


### Screenshots or Video

<details>
<summary>Screenshots / Video demonstration</summary>

[Upload media here]

</details>


### Logs

<details><summary>Logs</summary>

```console
[Paste your logs here]
```

</details>


### Flutter Doctor output

<details><summary>Doctor output</summary>

```console
$ flutter doctor -v
[✓] Flutter (Channel stable, 3.13.4, on macOS 13.5.2 22G91 darwin-arm64, locale en-CA)
    • Flutter version 3.13.4 on channel stable at /Users/uriravzin/development/flutter
    • Upstream repository https://github.com/flutter/flutter.git
    • Framework revision 367f9ea16b (2 days ago), 2023-09-12 23:27:53 -0500
    • Engine revision 9064459a8b
    • Dart version 3.1.2
    • DevTools version 2.25.0

[✓] Android toolchain - develop for Android devices (Android SDK version 33.0.2)
    • Android SDK at /Users/uriravzin/Library/Android/sdk
    • Platform android-33, build-tools 33.0.2
    • Java binary at: /Applications/Android Studio.app/Contents/jbr/Contents/Home/bin/java
    • Java version OpenJDK Runtime Environment (build 17.0.6+0-17.0.6b802.4-9586694)
    • All Android licenses accepted.

[✓] Xcode - develop for iOS and macOS (Xcode 14.3.1)
    • Xcode at /Applications/Xcode.app/Contents/Developer
    • Build 14E300c
    • CocoaPods version 1.12.1

[✓] Chrome - develop for the web
    • Chrome at /Applications/Google Chrome.app/Contents/MacOS/Google Chrome

[✓] Android Studio (version 2022.2)
    • 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 17.0.6+0-17.0.6b802.4-9586694)

[✓] IntelliJ IDEA Ultimate Edition (version 2023.1.5)
    • IntelliJ at /Applications/IntelliJ IDEA.app
    • Flutter plugin version 75.1.3
    • Dart plugin version 231.9392.3

[✓] Connected device (2 available)
    • macOS (desktop) • macos  • darwin-arm64   • macOS 13.5.2 22G91 darwin-arm64
    • Chrome (web)    • chrome • web-javascript • Google Chrome 116.0.5845.187

[✓] Network resources
    • All expected network resources are available.


```

</details>