I have this issue too with Windows 10 and iPhone 16 Pro. I want to try the iOS BETA to checkout the AI features but cannot backup my phone, presumably unless I use iCloud. I don't trust nor use iCloud. I have been using use iMazing local backups.
Neither Windows Explorer nor any software to backup the phone can see the phone when it is connected to my computer via USB. When I plug it into the computer, I get no message from Windows nor the phone. Normally you are asked if you trust the computer by the phone and the computer may ask how you want to use the device. In this case, nothing happens.
I have not tried with iTunes as I use iMazing. For QoF I had hoped never to open that software again forever, but I may give that whirl. The only thing I can see where this might help is if the iPhone 16's require drivers of some sort to be recognized by a computer system, maybe the USB implementation isn't completely standard and maybe the drivers are packaged with iTunes. Maybe Apple has new modern functional non-bloated app(s) to replace iTunes now??!?
I had read other threads that Apple support reported the lack of connectivity to the desktop for the iPhone 16 line is "by design". It's second and third hand info. I have also read a number of Mac threads that indicate the Macs have the same or similar issue. However the Mac folks found a work around where they can use a USB-C to USB-A converter cable and plug the USB-A into the Macbook (or a connected hub) and get it to work. My system only has one in-use USB-C which I have not tried yet, I have been trying with a USB-C to USB-A cable to no avail.