I really need to read posts properly. Somehow I missed half of the first sentence
The device checks to see if it can access a URL to see if the WiFi is working. If there is something blocking the URL, it will, in older firmware, drop the connection. More recent firmware will prompt whether to continue using it or not. The URL has also changed over the years. It originally used a Microsoft URL, but now uses a Kobo URL. So, exactly what firmware version the device is running is important.
I'll leave the what I originally wrote as the factory reset might make it relevant.
What firmware version did you have on the device? If it was running anything before 3.19.x, it will not be able to connect. This is because earlier in the year Kobo had to drop support of older protocols that were considered to be insecure. The currently supported protocols are in 3.19.x and later. The factory reset will have put an Aura back to a 2.x firmware. You will need to manually update the firmware or use the Kobo desktop application to do the setup.