I’ve skimmed through the known issues that stem from the currentl libfprint being unable to properly delete previous fingerprint registrations. I’m not sure if that’s only when those are made from Windows/this is a cross-OS issue, but in any case today I came across this problem when I replaced the SSD/reinstalled Fedora 35/restored /home/$USER.
It seems that there is some OS-side “credential material” stored in /var/lib/fprint/<user> which corresponds to entries stored in the Goodix reader which can’t be deleted properly, at least not if the new Linux installation hasn’t bootstrapped its credentials with the FP reader.
But you can still make your reader work in your new/additional Linux distro install if you keep these files and restore them to the new installation. This is an alternative to running the scripts (thanks @Devyn_Cairns!) that use patched libfprint.
So, just a note for search posterity. I don’t really understand the protocols used in these seemingly “secure enclave” type of FP readers, so take this with a grain of salt, but it worked for me.