With your 21.5-inch iMac running macOS 15.7, you can use the two external drives for different backup purposes.
Keep your existing external drive as the Time Machine destination.
macOS supports multiple Time Machine backup disks, so you could also add the unused drive to Time Machine.
Time Machine rotates among the configured disks and, when a particular disk is used again, backs up the changes since that disk was last used.
If you connect the second drive only periodically, its backup history will naturally be less current than the history on the continuously connected drive. (support.apple.com)
However, if your intention for the unused drive is to maintain a separate copy of your Mac's data and applications, rather than another Time Machine backup history, Carbon Copy Cloner (CCC) is another option. CCC can make an initial backup and subsequently update that backup with changes.
You can run it manually when you connect the drive or schedule it. CCC 7 supports macOS 15 and Intel Macs. (bombich.com)
There is an important qualification with macOS 15: CCC's normal startup-disk backup should not be described as a traditional, bootable, byte-for-byte clone of the entire macOS installation.
Apple's modern macOS system volume is handled differently from the Data volume, and CCC's standard backup focuses on the Data volume containing your applications, documents, settings, and other user data. (support.bombich.com)
Thus, the two-drive arrangement could be Time Machine on the existing drive for versioned backups and historical file recovery, and CCC on the unused drive for a separately maintained copy of your current data, applications, and settings.
You could keep the CCC drive disconnected except when updating it.
If instead you want the unused drive specifically to be another Time Machine destination, you do not need CCC; simply add the drive to Time Machine.
If you want an independent backup in addition to Time Machine, CCC provides a different backup method rather than merely duplicating Time Machine.
Apple's relevant documentation is Back up your Mac with Time Machine and Use Time Machine on your Mac to back up to multiple disks. CCC's documentation is available from Bombich Software.