Face ID Not Working [Fixed. Please see the approved answer for details.]

My problem is similar to yours except Face ID authentication has completely stopped working on iPhone 14 Pro running iOS 16.0.1, I get the message to enter account password to use Face ID then the next time I go to use 1Password I see the Face ID animation and a checkmark showing it was successful, but before the animation is over 1Password already has a message that says "That didn't work. Check your password and try again" resetting Face ID, toggling autofill off/on, deleting and re-installing 1Password, nothing fixes the 1Password Face ID authentication, it's stuck. Meanwhile Face ID works fine for everything else.