I think other commenters are missing your point: an iPhone should be able to back up to a "server" the same way a macbook does. I have a 24 TB NAS with Time Mac

I think other commenters are missing your point: an iPhone should be able to back up to a "server" the same way a macbook does. I have a 24 TB NAS with Time Machine on it so the phone should be able to backup to it (over wifi, usb, whatever) the same way it does to a Mac. And this should be possible out of the box by-design (not by using Linux based tools to backup the iPhone in ways Macs do not let you do).