New (unformatted) internal Seagate HDD not visible in Disk Utility for iMac 27"
If you place a totally uninitialized drive on macOS - it not only shows in Disk Utility and lets you partition it, but it prompts you to format the drive for use.

Something else is up in terms of firmware, cabling or perhaps settings on the drive itself. If Seagate tech support doesn’t have some obvious things to check - you’ll want to test it in another computer or on an external sled to be sure it’s working before returning it to the vendor.

Chances are it’s a cable that needs reseating on the logic board or on the drive itself. I know reseating the non drive end of the cable is a pain and replacing the internal SATA cable is a big pain - so try to test externally first if you can.

You probably know all the above since you mentioned independently verifying so here are some last ditch things:


Reset the NVRAM on the iMac (command option P R at boot)
Reset the SMC on the iMac (power down - disconect all power for 15 seconds)