Regardless of how you did it before, be aware that different backup methods will create different results on the second drive. Choose carefully based on how you want to use the external drive, and how you prefer to restore it in case the primary drive fails.
If your goal is to make the second drive an
exact copy of the primary drive — a drive you could potentially use as an
immediate drop-in replacement for re-linking a Lightroom Classic catalog to its referenced source files if the primary drive fails, use conventional backup software such as Carbon Copy Cloner, SuperDuper!, or ChronoSync that can make an exact “clone” of a folder or volume. An exact duplicate preserves all file paths on the backup, which is precisely what you want in a drop-in replacement.
If you use Apple Time Machine, the second drive becomes a
multi-versioned read-only backup, with folder versions stored as lots of virtual links to save space. The nice thing about this is that you can easily restore individual files and folders from your choice of past snapshots of backup dates and times. However, you cannot edit anything on a Time Machine backup because it’s strictly read-only…only Time Machine can alter it. In part this is to guard the backup against corruption by the user or by malware. But this also means a Time Machine backup can’t be used as a drop-in replacement for a failed drive. If your primary photo storage drive fails, a Lightroom Classic catalog won’t be able to relink to the originals until you tell Time Machine to restore a selected backup to a replacement volume. (I just tried relinking a catalog to a folder on a Time Machine backup, and the Update Folder Location command in Lightroom Classic won’t even list the folders in the Time Machine backup…which is correct behavior. The backup must be restored to a writable volume first.)
For these reasons, I use Time Machine to back up the Mac itself, but I use Carbon Copy Cloner to make an exact backup of the volume storing the source files that my primary Lightroom Classic catalog links to.
Also, if you value versioned backups, you can still have them even if you aren’t using Time Machine. Properly updated Mac backup software can also make and restore from APFS snapshots; for example
Carbon Copy Cloner can restore from its own snapshots.
You can also copy a whole volume by dragging and dropping everything in the Finder, but that’s more error-prone and almost impossible to update precisely after you add more files later. Backup software keeps track of what happened with logs, and can easily do an incremental backup.