iOS12 update bricked my iPhone 6S

I started the update to iOS12 on my iPhone 6s plus. When I looked at the screen, it showed the message:

Data recovery cannot be completed. Please restore your iPhone from backup.

Ok. So I plugged my iPhone into a Laptop running Windows 7 - the computer did not register the iPhone despite several attempts. So, I plugged the iPhone into a desktop running Windows 10. That did not register the iPhone as a device, despite several attempts, updating iTunes and running troubleshooters.

The Desktop registers my iPad ok, and runs iTunes. But not the iPhone.

I've reset the iPhone several times, but it just keeps displaying the same message.

How can I restore the iPhone from backup when it wont register as a device?