This is experimental, but I went ahead and ran the following after reading about it on reddit.

snap install fwupdmgr
/snap/bin/fwupdmgr install https://fwupd.org/downloads/cbe7b45a2591e9d149e00cd4bbf0ccbe5bb95da7-Synaptics-Prometheus_Config-0021.cab
/snap/bin/fwupdmgr install https://fwupd.org/downloads/3b5102b3430329a10a3636b4a594fc3dd2bfdc09-Synaptics-Prometheus-10.02.3110269.cab

These two cab files are referenced from:

• https://fwupd.org/lvfs/devices/com.synaptics.prometheus.config

• https://fwupd.org/lvfs/devices/com.synaptics.prometheus.firmware

Rebooted and then went ahead with the actual fingerprint setup:

After this was all done, login with fingerprints just worked. The only downside is that you need to press a key first to bring up the unlock logic.