Mac Catalina 10.15.7 Software update for IMac 27 (2012 model) Doesn't connect to Seagate 8TB backup

are using any of seagate's preloaded software on the drive that is supposed to make it "mac ready"? if yes, that could be the cause of your issue. when you use software from just about any manufacturer for their storage device you run the risk of that same software not being compatible with macOS updates / upgrades. it can cause the software to stop working. at best this will cause you a headache. at worst it can render your data inaccessible. it is always best to use disk utility to erase and format a drive before use to remove any preloaded software.

if you are using such software, i think your options are somewhat limited. 

you may want to contact seagate and see if there is an update for their software.

alternatively, if you have a backup you can revert your macOS to the version of catalina that the drive was working on and transfer your data to another storage device and then erase and format the seagate device before putting it back into service.

Erase and reformat a storage device in Disk Utility on Mac - Apple Support

File system formats available in Disk Utility on Mac - Apple Support

well, since you could access the drive after visiting seagate's download page, if it was me i would go to that seagate link again and use the steps you tried to see if you can once again access the drive. if successful then don't restart the mac. you can then move the files from the seagate drive to another storage device. then use the links i provided in my previous reply to erase and reformat the seagate drive before putting it back into service.