If you want to use parts of the Expo SDK in your existing React Native app, you are in the right place.
Most packages in the Expo SDK depend on a React Native module dependency injection and utility library called react-native-unimodules. Once it is installed and configured in your app, you can install other packages from the Expo SDK just as you would any other React Native library.
The reason react-native-unimodules exists is so that we can reuse native code across Expo modules to reduce code duplication, improve reliability, and provide a consistent API across modules. For example, Camera can use native code from FileSystem and Permissions rather than Camera reimplementing the functionality those modules provide.
The short version: find an Expo package that you would like to use in the API reference or by searching this documentation, eg: expo-web-browser,install it with npm, then run npx pod-install and re-build your app.
You're ready to go. You may also want to install expo-updates in your app to add support for over-the-air-updates. If so, follow the installing expo-updates guide guide once you have installed react-native-unimodules.