I have purchased a new external backup drive. When I add it as a time machine backup volume, I am not offered the option to encrypt the backup.

I also have the same issue. I do not see a choice to encrypt when I set up the Time Machine backup disk. I am using a 1TB Seagate Expansion Drive for a few years, which has worked fine with Time Machine, except that I cannot encrypt it.

The encryption window will not show up if the disk does not support encryption. The user guide for Ventura 13 says "Note: A window appears if your disk supports space limits and encryption for backups." See Connect a new backup disk to your Mac - Apple Support

Perhaps my drive is not one of those supporting encryption? I would like to find out which drives support encryption in Time Machine. The user guide says that some storage disks "don't support" Time Machine. "Note: Some network disks from manufacturers other than Apple don’t support Time Machine. If the disk doesn’t appear in the list of devices available for Time Machine backups, contact the disk’s manufacturer." See Types of disks you can use with Time Machine on Mac - Apple Support (at the bottom of the page). I thought to look at the "list of devices" to see if mine appears, and if not, obtain a drive that does appear on the list. There is a user guide page that generally discusses the types of disks that support Time Machine. However, as to the "list of devices" it references, I cannot find any such list.

Any suggestions re encryption or that "list of devices"?

I think this link will help you with your desire to encrypt your backup with Time Machine --> Keep your Time Machine backup disk for Mac secure - Apple Support

You don't see this when you click Setup disk…

What is an "expansion drive" as opposed to just any drive?