In Fedora it's (supposed to be) pretty simple. Just go into settings -> users and add your fingerprint. In practice I usually have to use dnf to nuke pam and reinstall it manually for it to start working. But they have a good skeleton set up. Still no predesktop authentication, though.
I thought yubikeys only provided a sensor for the fact that the sensor was touched, vs fingerprint resets that actually distinguish whose fingerprint is touching the sensor before being usable as an authenticator
most of them only have touch sensors but the yubikey bio series devices have actual fingerprint readers, and as part of the device setup you register one or more fingerprints which are then stored on the device itself