I had an unusual experience that I would like to document here.
I have an iPad Mini 2 given to me that had this exact error message when using a Mac.
When moved to a PC, it gave an "Unknown error 3194."
When loaded from Software Update on iOS, I got a dialog box during the "Verifying Update" process that reported that my connection to the Internet was lost (which was not true).
The exact message is:
Unable to Verify Update
iOS 12.5.7 failed verification because
you are no longer connected to the
Internet.
After hours of thrashing, I tried to open a case with Apple, only to discover that the serial number of this device was not recognized. So, I opened the case using another device's serial number.
After some time on the phone, we discovered that both my serial number and IMEI were not on file at Apple! The signing server was rejecting my request to upgrade since my device was not recognized.
Now, before anyone asks, the serial number shown in IOS matched the one etched on the case, so there was no activation-lock-bypass hacking going on here.
The recommendation? Go to the Apple Store and have the register the serial number into the systems. I will do that in the next few weeks and will report back. Of all of the answers I found on this topic, NONE of them suggested that the serial number might be missing from Apple's databases. As a result, I leave this message here for future travelers experiencing this issue.
Try to open an Apple support case using the serial number of your device. If the serial number is not recognized, that's a strong clue that the device may experience this problem.