Assumptions:

• You have fprintd installed already, following the Arch wiki.
• You have enrolled your fingerprints.

Install polkit:

sudo pacman -S polkit

Create a polkit-1 file in pam.d:

sudo nano /etc/pam.d/polkit-1

#%PAM-1.0
auth       sufficient   pam_fprintd.so
auth       include      system-auth
account    include      system-auth
password   include      system-auth
session    include      system-auth

Testing:

pkexec whoami

You should see the system authentication prompt and it should prompt for your fingerprint as well.

To Bitwarden:

In Settings -> Security, check “Unlock with system authentication”. Then close the settings and lock the vault with either the menu item or Ctrl+L.

You should see “Unlock with system authentication” above “Unlock with master password”.

Give it a click. You should get the same prompt as before from pkexec and it should include the fingerprint request.

To 1Password:

In Settings -> Security, check “Unlock using system authentication service”. Then repeat the prior steps for Bitwarden.

This all just worked for me, so I have no idea what to do if it goes wrong for you, dear reader.