I got the SD image, had to put it on the card with Rufus because neither of the recommended tools can se any devices on Windows 10 x64.
Booted up the Kobo WiFi, which it did quickly. It's not a clean image (has someone's email address) and it's version 1.9 instead of the final 1.9.12.
Is version 1.9.12 listed here for Kobo Touch A/B also for the N647 WiFi?
https://pgaskin.net/KoboStuff/kobofirmware.html
But at least it's working again, sort of. Still hiding the FAT32 partition from Windows (shows as unallocated in disk management), still not detected by the Kobo plugin in Calibre. Still not detected by the Kobo Desktop software.
Edit: I connected the Kobo to a different PC, same version of Windows 10, and it's detected properly by Windows and the Kobo plugin for Calibre.
So something on my desktop is quite specifically interfering with the Kobo, the Vconsole image writer, Alexander Beug's image writer,
and only those three things. Every other USB device I have works with this PC, and I have a lot of USB things. Every other software I have that uses USB works without a problem.
Edit2: I removed all 3rd party USB controller and hub drivers, letting Windows install Microsoft provided drivers. No change. No Kobo detection, neither of the USB image writers detect any writeable devices.