I tried to do this I can’t get it to fully prevent EAS / Expo from calling home.
I do run the builds locally so at least it uses proxied repositories. The final bit of delivering to Apple/Google is managed by another build stage with separate credentials.
Push notifications do not need Expo either, but you’d be responsible to set up the communication channel to Google FCM or Apple Push Notifications. It’s not too difficult from what I can tell, just didn’t make the time to migrate away yet.
I also explicitly disable the “updates” functionality and rely on a proper upload per version to the app store (it may mean the updates are bigger because it’s a full app, but it’s under my control). Note you’re still forced to have expo-updates turned on if you want to prototype using Expo Go from what I can tell (or at least it nags me everytime I try to do expo publish).
However, there does not appear to be any way to fully decouple yourself from using Expo’s systems.