You register a device (authenticator), which generates and registers a new public key. You show up with that again in the future, which answers a challenge by using the private key. So it's just saying "I'm the same device as you've seen in the past".

The system QR code behavior is for when your registered credential lives on another device. It sounds like you might have not registered anything yet, so you don't have any account or credentials with which to sign in.

In the specific case of Apple, your PassKey is stored in iCloud, and so can be retrieved from any Apple device you are signed into.

Without this kind of cloud sync, you need at least two devices, or you will be locked out if you lose or break one.

You can also save it to your phone, you only need to scan another QR code if you want to save it on another device

I’m given a prompt to either use another device or an external key. Those are the only two choices. Or am I supposed to create via email first and that’s what I’m missing?

You have to create first.

Do you use fingerprints to unlock your device? The page asked me to identify via fingerprints