External HDD Activity – Why is External HDD Active When Not in Use?

I think what you could do is creating a encrypted disk image on the external HDD and put your time maschine files in it for the timeframe your friend has the disk. To achieve this open the disk utility tool and choose File -> New -> Blank Disc Image (or Image From Folder).

BUT keep in mind that as long as this disk is not (re-)formatted properly it will be easy to recover unencrypted data which seems to be deleted or moved (using some fancy recovery tools).

Time Machine cannot backup to an APFS disk, because APFS doesn't support hard-linking, which is essential to Time Machine's operation.

From Apple KB - Types of disks you can use with Time Machine on Mac

Important: You can back up from an HFS+ or APFS-formatted disk to an HFS+ disk; however, Time Machine can’t back up to an APFS-formatted disk. If you select a back up disk formatted as APFS, Time Machine offers to reformat it as HFS+.