Add RN Expo background sync example (#269)

Author: cahofmeyr

usage/use-case-examples/background-syncing.mdx

@@ -10,9 +10,10 @@ Applications often need to sync data when they're not in active use. This docume
 Background syncing has been tested in:
 
 - **Flutter** - Using [workmanager](https://github.com/fluttercommunity/flutter_workmanager/)
+- **React Native & Expo** - Using Expo's `BackgroundTask` API. See our [demo](https://github.com/powersync-community/powersync-react-native-expo-background-sync) and accompanying [blog post](https://www.powersync.com/blog/keep-background-apps-fresh-with-expo-background-tasks-and-powersync).
 - **Kotlin Multiplatform - Android** - Implementation details in the [Supabase To-Do List demo](https://github.com/powersync-ja/powersync-kotlin/blob/main/demos/supabase-todolist/docs/BackgroundSync.md)
 
-These examples can be adapted for other frameworks like React Native. For implementation questions or assistance, chat to us on [Discord](https://discord.gg/powersync).
+These examples can be adapted for other platforms/frameworks. For implementation questions or assistance, chat to us on [Discord](https://discord.gg/powersync).
 
 ## Flutter Implementation Guide