Toshiba canvio only format choice is nfps. Mac OS ventura on macbook air M1 2020

APFS or APFS encrypted would be typical for use with Time Machine on recent macOS configurations:

… Types of disks you can use with Time Machine on Mac - Apple Support

For using Disk Utility:

… Intro to Disk Utility on Mac - Apple Support

… File system formats available in Disk Utility on Mac - Apple Support

Again, Time machine wants the whole storage volume.

Toshiba apparently has various products using the Cancio name, so I’m nor sure which is in use here. From a very quick product search, Canvio Connect, Cancio Advance, Canvio Basics, and probably some others.

APFS or HFS+ would be typical storage volume formats used with macOS.

NTFS is a Microsoft format, and macOS can read that, but not write.

If you cannot reformat the exteranl storage to APFS or HFS+ using Disk Utility(and that should work), you’re left to return the storage for a refund and acquiring some alternative, or acquire an add-on NTFS app such as Paragon.

Time Machine does not support NTFS. Time Machine wants the whole device or whole partition, too.

I’m familiar with a feature known as “drag and drop”, but not with “dragon drop files” and related requirements.

You could conceivably partition the storage, though how well that works will all that’s apparently in use here?