iMac not recognizing Seagate drive after Tahoe update

Open Applications > Utilities > Disk Utility, select View menu > Show all devices. Does it show up there, and if so, can you mount it?

There were a few prior posts on this forum from users who couldn’t access their external drive due to the drive manufacturer’s software that they used to encrypt the drive. Lacie/Seagate, Samsung, SanDisk, etc., all provide 'drive management' software on their drives and using such 3rd party software can cause issues when macOS is updated and the 3rd party software becomes incompatible. Not sure if that's theissue here, but FYI the best practice with a new external drive (SSD/HDD, not applicable to NAS drives) is to use Disk Utility to complete erase it, format it as GUID/APFS and apply encryption if desired.

Have you tried Disk First Aid?

If it’s just a TM backup, personally I’d erase/reformat and keep using it, assuming it checks out ok with First Aid.

Seagate owns LaCie, I think. I’ve used both, I have a stack of LaCie Rugged HDDs in a closet, they still work but I’ve switched to a pair of Samsung 4 TB SSDs for my secondary TM backups (primary is a 2x10 TB NAS).