External LaCie Backup Drive Not Recognized

How can I get my backup drive to a) show up in Finder as a device; and b) be listed in Time Machine as an optional location for my backups?

Deets: MacBook Pro 2017 13-inch, processor 2.3 GHz dual core Intel i5, two USB-C Thunderbolt 3 ports, OS Catalina 10.15.4.

When I purchased the LaCie 1TB Rugged USB-C Mobile Storage from the Apple Store for backing up my laptop, I connected it via the LaCie USB-C cable that came with the drive. The drive status light turns on, but does not stay on forever (approximately 15 minute stints).

In first connecting the backup drive, I initially received a popup asking how I wanted to format the backup files. I clicked "as on the laptop", but received an error message that the laptop file format was incompatible with the drive's format. Since then, I do not see the LaCie drive listed in Devices in Finder or as an optional location in Time Machine. External Disks is checked to show up in Finder preferences. When I click Select Backup Disk in Time Machine preferences, the only option listed is Other AirPort Time Capsule.

Please advise, as I would like to back up to a hard drive (in addition to the iCloud) before using Boot Camp to allow booting up using Windows (an unfortunate requirement by my employer to be able to work from home). Many thanks.

[Image Edited by Moderator to Remove Personal Information]