expo-sdk-53 upgrade not writing clientId to build.gradle via plugin → Build Failure

After upgrading our project to Expo SDK 53, we noticed that the plugin responsible for injecting clientId into android/app/build.gradle is no longer working.

Previously (Expo SDK 52 and below), the plugin correctly appended the required clientId configuration into the Gradle file. But after upgrading, the line is not being written, which results in a build failure since the clientId is required during compilation.

### Steps to Reproduce:

- Upgrade project to expo-sdk-53
- Run expo prebuild / eas build -p android
- Inspect android/app/build.gradle → clientId is missing
- Build fails due to missing clientId reference

### Expected Behavior:
The plugin should continue to correctly inject clientId into build.gradle after upgrading to Expo SDK 53.

### Actual Behavior:

- No clientId line is added to build.gradle.
- Android build fails with clientId not found error.

### Environment:

- Expo SDK: 53
- EAS CLI: 15.0.12
- Platform: Android

Start at the Expo plugin entry point and reproduce the issue with Expo SDK 53 using expo prebuild or eas build -p android. Inspect the generated android/app/build.gradle and compare it with the expected clientId configuration. Done means the plugin writes the clientId line and the Android build no longer fails because it is missing.

Written by the indexing model from the issue text.