serial number unavailable

If it's possible it might have happened when I factory reset it.

It shouldn't. The serial number shows a couple of places. Obviously in "About this Mac..." whihc can be flaky form other infor, but have you looked at System Information? You get that report by clicking the "System Report..." button at the bottom of the "About this Mac..." window. The SI report's first screen, "Hardware Overview," should show the number as well:

The serial number should also available by command line in Terminal. See:

https://osxdaily.com/2011/04/25/get-mac-serial-number-command-line/

It is best to copy and paste the commands due to the command line's demands for respecting spaces.

Has it been serviced, specifically had a new logic board installed?

If a tech replaced the logic board and omitted the important step of transferring the serial number to the firmware on the new board, you can get no serial number when y udo "About this Mac..."

If that is the case, whoever serviced it should correct their error.

The serial number on a 27-inch iMac is also on a sticker on the underside of the "foot" of the metal stand.

You are most welcome.