The login information is securely stored in the iOS keychain subsystem. Unlike macOS, the keychain in iOS is not accessible to the user. However, applications can programmatically store and query data in a keychain.
Apps developed by Google search for pre-existing user information in the iOS Keychain during installation. Login information is not removed from the device unless you choose to remove the account of your device from one of the installed applications.
The iOS keychain provides a secure cryptographic disk store that is locked when the device is locked and unlocked when the device is unlocked. An application can only access its own keychain items or those shared with a group to which the application belongs. Applications from the same developer, such as Google in this case, belong to the same group (via the common component Bundle Identifier), which allows them to share a secret via the keychain.