

I’m pretty sure it’s possible to use timeshift to create backups on another drive using rsync (instead of btrfs). They are incremental, and deduplicated, as well.
But the other commenters are correct, timeshift is not a backup tool, it’s more for snapshots to undo system changes you may not want. In addition to that, it doesn’t do user files by default — because again, it’s not a backup tool.
btrfs send/receive
technically does what you want, using btrfs to do backups to another drive, but I don’t think any GUI app supports it. Plus, you would have to create snapshots for btrfs from the command line.
Your best bet are apps explicitly designed for this usecase, like someone mentioned pika, or borg or restic are good choices. They don’t do BTRFS, but they do incremental, deduplicated updates in a user friendly way.
Depends on the program and the professors. I’m doing computer scuence at CSUN, and I’ve gotten lucky, none of the online exams have required any proctoring software (rootkit monitoring software). They just do them in the browser.