Two options, each configurable by the developer implementing the SDK:
(1) When a user sets up their new phone using an iCloud / Google Drive backup of their old phone, the private keys will be already embedded in the relevant apps when they first open the app on the new phone. The developer can ask the user to decrypt the private key for the first session with a user-defined passcode
(2) The SDK provides a QR backup system - users can export their private key in a QR code, print it out or save it on a USB drive, and then scan that code using their new phone. Alternatively, they can just open that QR backup screen on their old phone and scan that with the same app on their new phone. Google Authenticator recently released a key export feature like this (we had it before Google, but it's inspired by blockchain.com's wallet backup system from 2012).
Correct, that's currently the case. Users can use QR code backup/restore functionality if enabled by the developer to switch between iOS and Android. That would have to be done app-by-app. We're working on our own cloud backup system to automate this.
I think such transitions between smartphone OSs already entail significant credential transfer issues, since saved passwords also do not automatically move between OSs.
You'd have similar problems if you used "Sign in with Apple" for an app on an iOS device and then switched to Android.
(1) When a user sets up their new phone using an iCloud / Google Drive backup of their old phone, the private keys will be already embedded in the relevant apps when they first open the app on the new phone. The developer can ask the user to decrypt the private key for the first session with a user-defined passcode
(2) The SDK provides a QR backup system - users can export their private key in a QR code, print it out or save it on a USB drive, and then scan that code using their new phone. Alternatively, they can just open that QR backup screen on their old phone and scan that with the same app on their new phone. Google Authenticator recently released a key export feature like this (we had it before Google, but it's inspired by blockchain.com's wallet backup system from 2012).