Expo-updates Issue: Empty String Returned from Updates.channel on Android

### Build/Submit details page URL

_No response_

### Summary

I am encountering an issue with the expo-updates library in my Expo project specifically on Android. Despite configuring the project correctly, I am getting an empty string when trying to access the Updates.channel.

This issue happened after I did the migration from Expo Classic Updates

### Managed or bare?

Managed

### Environment

expo-env-info 1.0.5 environment info:
System:
OS: macOS 14.1
Shell: 5.9 - /bin/zsh
Binaries:
Node: 14.19.2 - ~/.nvm/versions/node/v14.19.2/bin/node
Yarn: 1.22.18 - /opt/homebrew/bin/yarn
npm: 6.14.17 - ~/.nvm/versions/node/v14.19.2/bin/npm
Watchman: 2023.12.04.00 - /opt/homebrew/bin/watchman
Managers:
CocoaPods: 1.14.3 - /opt/homebrew/bin/pod
SDKs:
Android SDK:
Android NDK: 22.1.7171670
IDEs:
Android Studio: 2022.2 AI-222.4459.24.2221.9971841
Xcode: /undefined - /usr/bin/xcodebuild
npmPackages:
expo: ^48.0.0 => 48.0.21
react: 18.2.0 => 18.2.0
react-dom: 18.2.0 => 18.2.0
react-native: 0.71.8 => 0.71.8
react-native-web: ~0.18.7 => 0.18.12
npmGlobalPackages:
eas-cli: 6.0.0
expo-cli: 6.3.10
Expo Workflow: managed

### Error output

_No response_

### Reproducible demo or steps to reproduce from a blank project

**eas.json**

```
{
"cli": {
"version": ">= 0.48.2"
},
"build": {
"development": {
"channel": "development",
"ios": { "image": "macos-ventura-13.3-xcode-14.3" },
"android": { "image": "default", "buildType": "apk" }
},
"staging": {
"channel": "staging",
"ios": { "image": "macos-ventura-13.3-xcode-14.3" },
"android": { "image": "stable" }
},
}
```

**command to build**

`eas build --profile staging`

**On the project. I fetch the channel by**

`import * as Updates from 'expo-updates';`
```

console.log({
channel: Updates.channel,
});
```
**output**

`channel: ""`