I’d be very surprised if anything, including the enrollment, happened off the device. Likely all it involves is sending a “register my fingerprint now” message

I’d be very surprised if anything, including the enrollment, happened off the device. Likely all it involves is sending a “register my fingerprint now” message being sent to the YK, you touch it, then the YK works as expected. They already provide a Linux-native “YK management” program, presumably it just needs to be updated.