I think "spying" implies "everywhere possible", including, outside the app

My hope is: no way for latest public update

I think that if your iOS version is latest and some basic code to unlock your phone is set and even if you're not logged in, it will not make storage available because you wouldn't be able to set the options to up backup your data, besides allowing it

I mean did you have some sort of code (I cannot remember the name) set. Or what did you see if screen is off and you hard reset it, or at least soft reset, or just locking it with power button and waking in up the same way?

Try to ask support in a technical manner. Provide ID if asked

Hard to tell with Apple stuff. The idea on the "way of getting it to device to run persistently, not until reboot" is quite different too often. There was Pegasus