Is there any existing software that replaces the GUI password dialogue with something else like phone authentication? That is, instead of typing the password in the dialogue box below, you click “Authenticate” on the phone or touch the fingerprint sensor of the phone.
Not normally. UNIX authentication is text-based and relies on a salted hash for every user account in /etc/shadow, or via a server-based centralized authentication framework such as OpenLDAP.
Maybe there’s something close in there.
https://wiki.archlinux.org/title/Category:Authentication