I have a Lenovo that has the same fingerprint reader built into the power button. The following link is the method I have shared on this forum that it working for my laptop.
https://askubuntu.com/a/1488580/1737945
How to enable 0c4b ELAN FingerPrint Driver for Ubuntu 22.04 64bit. A common fingerprint reader on Lenovo laptops.
Confirm the device in a terminal.
$ lsusb |grep Elan
Bus 003 Device 002: ID 04f3:0c4b Elan Microelectronics Corp. ELAN:Fingerprint
or
$ hwinfo | grep Fingerprint
Device: usb 0x0c4b "ELAN:Fingerprint"
After confirming your device is the 0c4b, download the drive from the Lenovo support site.
Google search: "ELAN FingerPrint Driver for Ubuntu 22.04 - ThinkPad E14 Gen ..."
or
use the following link: https://support.lenovo.com/us/en/downloads/ds560939-elan-fingerprint-driver-for-ubuntu-2204-thinkpad-e14-gen-4-e15-gen-4
Download the driver "ELAN FingerPrint Driver r1slf01w.zip"
The site will ask for a serial number on the first try, ignore this by clicking cancel on the pop-up screen & click download again. On the second try it will download the zip file without the popup asking for a serial number.
Extract the zip file & open a terminal in the extracted folder. The only contents of the folder should be "libfprint-2-tod1-elan.so".
In the terminal:
(Assumed location of download, may be different on your system)
$ cd ~/Download/r1slf01w/libfprint-2-tod1-elan_0.0.8_Ubuntu22.04
(best practice before any new install of applications)
$ sudo apt-get update && sudo apt-get upgrade
(This installs the fprint library & ssl tools. Note that libssl3 should already be installed on Ubuntu 22.04 fresh install, so may be no need to install libssl3)
$ sudo apt install libfprint-2-tod1 libssl3
(Create a directory for the system to access the driver)
$ sudo mkdir -p /usr/lib/x86_64-linux-gnu/libfprint-2/tod-1/
(Copy the driver into the new folder)
$ sudo cp libfprint-2-tod1-elan.so /usr/lib/x86_64-linux-gnu/libfprint-2/tod-1/
(Restart the fprint service to load the new driver)
$ sudo systemctl restart fprintd.service
(Exit the terminal)
$ exit
Go to settings, select "Users" & enable "fingerprint login". Click the marker to the right of "Enabled" & Enroll fingerprints.