Can I use two factor authentication on an iPhone without a phone number?

I got a new iMac a few months ago. I wanted to get a magic keyboard with Touch ID, but it doesn't work with the model of iMac I bought (It works with Apple M1 processors. Mine has a nice Intel one). I thought I might be able to do something similar with an old iPhone 5 I have. It's not hooked up to a phone number anymore.

Can I use the the two-factor authentication using Bluetooth or Wi-Fi without phone number?

I love the idea of being able to use one of my old iPhones as a fingerprint reader for my new iMac. Is it possible?