Use fprintd
https://wiki.archlinux.org/title/Fprint
sudo
in /etc/pam.d/sudo just add to the top:
auth sufficient pam_fprintd.so
polkit
For GNOME prompts, first install pam-fprint-grosshack if you want to be able to user fingerprint or a password and add to the top of /etc/pam.d/polkit-1:
auth sufficient pam_fprintd_grosshack.so
auth sufficient pam_unix.so try_first_pass nullok
gdm
GDM has built in fprintd support