What I feel like all the responses missed is that while you're right in that a password-protected private key provides a second factor... what is typically meant by 2FA is two factors checked by the server. The server has no way to know you're using a password-protected key so it shouldn't really be regarded as a factor.

You are incorrect. The only factor used there is the key. The password simply decrypts the key to perform the requested authentication.

2FA would be private key (password-protected) and a separate (most likely one time use) password. Something you have (key that you decrypted) and something you know (the one-time password).

No.

Keys are easily (and persistently) added to ssh-agent, at which point it is easy to forward and will generally silently authorize without any further user interaction. That reduces it to a single factor.

Compare that to a totp challenge or a yubi key plus a password. Having one of them won’t get you the other.

If the private key cannot be read by anyone and the user must authenticate to get the device to sign the authentication request, then it could be considered 2 factor by some interpretations.

The problem with that is that your users can always generate a key without a passphrase at all and you have no way of knowing

The author probably meant "two-step" (out of band verification) rather than two-factor.