Backing up / in it’s entirety might cause issues since there will be a lot of special files and crossed mount points. You should probably exclude /proc and any system folders from the backup. See: github.com/bit-team/backintime/blob/dev/FAQ.md#do…
Since you’re planning to start with a clean Nobara install, you can probably exclude those during the restore step. Just be careful not to restore files that are in active use by the running system.
Have you tested restoring from your backup? Can you do it from the liveUSB?