The USB id of the fingerprint reader on X1C6 is 06cb:009a while on X1C7 it is 06cb:00bd.
This is the list of supported devices: https://fprint.freedesktop.org/supported-devices.html
As you can see the one for X1C7 is supported, X1C6 unfortunately isn't.
This is their gitlab issue for it: https://gitlab.freedesktop.org/libfprint/libfprint/issues/13...