I'd like to think that the old TiBackup method would have worked for your cameras. It tried to save the applications along with their data -- including old, online auth data. Almost all of my stuff Just Worked after using it.

At very least it was way, way better than the wink-and-a-smirk, blind, opaque, vague-handwaving "Your phone is backed up on Google servers!" process that we have these days, wherein: As a practical matter, if I can't touch the backup to examine it, or exercise it at my whim, then that backup doesn't meaningfully exist.

But as I understand it: Your problem is deeper, and riskier. You can't goof around with these existing phones in any way. If you poke at one and the closed-source black-box app decides that it is unhappy, then that means that there is one fewer phone in the world that can do the things you need to do with your cameras.

Maybe the best answer for you is to leave those phones alone, and get another phone you can hack on for the express purpose of trying to to get the camera working on it. This takes the risk out of the loop.

Maybe that means something that passively monitors data over the USB connection and putting together a new app that operates the camera in the same way.

Or perhaps beginning that process would allow recognition: Maybe it's already using a bog-standard protocol on the wire to talk to the camera and it's NBD to download another app that works with your cameras on any new, random phone.

Maybe it instead involves a patch for your existing app's APK that bypasses the authentication step, and this can then be used on a different phone.

Whatever form this liberation takes, it is the kind of thing that a person of adequate skill, or with the right kind of wit and a good LLM, or all of these together, can almost certainly solve. (It might even be easy.)