[Bug]: `checkPermission()` does not reflect correct state after granting permissions via `requestPermission()` in Safari.

### Please check the following before submitting a new issue.

- [X] I have searched the [existing issues](https://github.com/baseflow/flutter-geolocator/issues).
- [X] I have carefully [read the documentation](https://github.com/Baseflow/flutter-geolocator/blob/main/geolocator/README.md) and verified I have added the required platform specific configuration.

### Please select affected platform(s)

- [ ] Android
- [X] iOS
- [ ] Linux
- [X] macOS
- [ ] Web
- [ ] Windows

### Steps to reproduce

* Grant permissions to Safari within the `Settings` app
* Mac OS: System Settings > Privacy & Security > Location Services (ON) > Safari (ON)
* (iOS): Settings > Privacy & Security > Location Services > Safari > While Using the App
* Execute your Flutter web in Safari
* Within your code, add some workflow that will trigger the following workflow:
```
...
var currentPermission = await Geolocator.checkPermission();
if (!isLocationPermissionGranted(currentPermission)) {
await Geolocator.requestPermission(); /// Grant while-in-use
}
currentPermission = await Geolocator.checkPermission();
assert(currentPermission, LocationPermission.whileInUse);
...
```

Tested in:
- Safari desktop 17.1.2
- geolocator plugin v10.1.0

### Expected results

The assertion should pass in all supported platforms.

### Actual results

This fails in Safari (desktop and mobile).

### Code sample

Code sample

```dart
...
var currentPermission = await Geolocator.checkPermission();
if (!isLocationPermissionGranted(currentPermission)) {
await Geolocator.requestPermission(); /// Grant while-in-use
}
currentPermission = await Geolocator.checkPermission();
assert(currentPermission, LocationPermission.whileInUse);
...
```

### Screenshots or video

_No response_

### Version

10.1.0

### Flutter Doctor output

Doctor output

```console
[✓] Flutter (Channel stable, 3.13.9, on macOS 14.1.2 23B92 darwin-arm64, locale en-CA)
• Flutter version 3.13.9 on channel stable at /Users/jdbenito/development/flutter
• Upstream repository https://github.com/flutter/flutter.git
• Framework revision d211f42860 (8 weeks ago), 2023-10-25 13:42:25 -0700
• Engine revision 0545f8705d
• Dart version 3.1.5
• DevTools version 2.25.0

[✓] Android toolchain - develop for Android devices (Android SDK version 34.0.0)
• Android SDK at /Users/jdbenito/Library/Android/sdk
• Platform android-34, build-tools 34.0.0
• ANDROID_HOME = /Users/jdbenito/Library/Android/sdk
• Java binary at: /Applications/Android Studio.app/Contents/jbr/Contents/Home/bin/java
• Java version OpenJDK Runtime Environment (build 11.0.15+0-b2043.56-8887301)
• All Android licenses accepted.

[✓] Xcode - develop for iOS and macOS (Xcode 15.0)
• Xcode at /Applications/Xcode.app/Contents/Developer
• Build 15A240d
• CocoaPods version 1.14.3

[✓] Chrome - develop for the web
• Chrome at /Applications/Google Chrome.app/Contents/MacOS/Google Chrome

[✓] Android Studio (version 2022.1)
• 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 11.0.15+0-b2043.56-8887301)

[✓] VS Code (version 1.85.0)
• VS Code at /Applications/Visual Studio Code.app/Contents
• Flutter extension version 3.78.0

[✓] Connected device (4 available)
• sdk gphone64 arm64 (mobile) • emulator-5554 • android-arm64 • Android 13 (API 33) (emulator)
• JD Personal iPhone 13 Pro Max (mobile) • 00008110-001068C226A1801E • ios • iOS 17.1.2 21B101
• macOS (desktop) • macos • darwin-arm64 • macOS 14.1.2 23B92 darwin-arm64
• Chrome (web) • chrome • web-javascript • Google Chrome 120.0.6099.109

[✓] Network resources
• All expected network resources are available.

```

Start by reproducing the permission workflow in Safari desktop and mobile using geolocator v10.1.0, comparing the values returned by checkPermission() before and after requestPermission(). Done means the assertion reports LocationPermission.whileInUse after permission is granted in Safari while preserving the expected behavior on supported platforms.

Written by the indexing model from the issue text.