Same or similar problem here.
Fresh Fedora 35 installation.
Installed Timeshift throug software manager gui. Starting with no error but not able to select any disk space due to not showing anything in the location tab.
Reinstalled with sudo dnf command. Seemed to install correctly but I can not start the gui. Just on the terminal it responds.
EDIT:
After just trying with sudo timeshift gui
I now have a timeshift icon in gnome but when starting same issue with no location visible.
EDIT 2:
Timeshift says it´s running in “live-usb-modus”. That´s not as intended I guess. ^^
EDIT 3:
Managed to install latest Timeshift version that works. Needed to do sudo dnf clean all
.