I'd wondered if it was possible to do a Time Machine backup to a cheap Flash Drive. My daughter is going to college and probably doesn't have a great need for backup (iCloud Document/Desktop, iCloud Photo, Google Docs, etc) but I'd still like to do something.
So I wondered about a compact Flash Drive. In the twilight of the web Google couldn't find me an answer, so I ran my own test. I used an old San Disk Ultra Fit 128GB USB 3.0 Flash Drive in an old USB 2 MacBook Air running High Sierra. I formatted the Flash Drive as encrypted HPFS and let Time Machine run the backup.
It took about 4-5 hours to do the initial 80GB backup but it seemed to work fine.
I doubt these Flash Drives are super reliable, but I think this is an option. I can see taking advantage of it while traveling for example. Unfortunately her 2020 Air doesn't have an open USB slot where an Ultra Fit could live, but it could be a part of her Anker 7-1 USB-C docking station. A modern San Disk Ultra Fit USB 3.1 is $33.