Oh, I am so glad (well I guess not really... misery love company?) to see I am not the only one having this problem. I have posted about it elsewhere in these forums.
I updated to Catalina and random shutdowns ensued only when the Thunderbolt (1) drives I used for TM backups were mounted. Tried various fixes, clean install, fresh backups, many calls to Apple Support... eventually bringing the iMac into my Apple Service Provider, along with the external hard drives I used for backups, both of which were connected via the Thunderbolt 1 interface (one of them via a Thunderbolt to Firewire adapter). They rebuilt (as it were... cleaned up) the iMac Fusion Drive, redid the clean install, and tested both external hard drives, reformatting one of them (at some cost). They could find no hardware issues with the iMac.
Problem persisted with random shutdowns when external hard drives were mounted. So replaced both with new USB external drives... no more shutdowns. Griffin replaced the G-Drive Pro Thunderbolt along with a new Thunderbolt cable under warranty. I retired the other older WD drive (firewire connected via a Thunderbolt adapter). But problem persists.
Then I did another clean reinstall, migrating only User Data over (no Applications or Network Settings) to see if this would fix it. Problem persists only when the Griffin G-Drive Pro Thunderbolt is mounted, random crashes (shutdowns), not when the two USB external drives are mounted.
There is no Firmware update for the G-Drive that I could find (oh, and I reset the SMC and NVRAM... not the cable, but it has happened with two separate cables... could they both be bad?).
Apple says it must be a hardware issue since I've done all I can, but I have a feeling Catalina is not playing nice with the Thunderbolt interface or just the G drive architecture somehow. The problem only surfaced with Catalina.
Love to know if anyone else has gotten any info on this.