I guess one option would be to ask the victim to read out the token from memory or disk. That seems pretty hard though. It's debatable whether that would be considered credential phishing.
A more likely method would be to trick someone into going into devtools and copy and pasting something from there, possibly a curl command, like in this epic "bug report"[1]. That's also debatable whether it would be credential phishing.
This FIDO authenticator has absolutely no idea what your per-site keys are. Instead, the random-looking ID provided to the site when you register and then given back by the site when logging back in actually is your private key for that site... encrypted using AEAD with symmetric keys only the FIDO authenticator knows.
One of the ingredients for decrypting the key is rpIdHash which is SHA256(dnsName) where dnsName is the FQDN of the site you're looking at or some suffix of that FQDN chosen by the site. So here it could be news.ycombinator.com or ycombinator.com (Public Suffixes like com or co.uk are prohibited). The browser is responsible for calculating rpIdHash.
Thus on a phishing attempt usually the AEAD fails, the authenticator not only doesn't give the phishing site a signature that can be used to sign in on a different site, it will ignore this ID and act as though the user doesn't have a FIDO authenticator plugged in at all.
I guess you would need to ring someone up pretending to be tech support and convince them to disclose the private key.
But a practical attack along the lines of what you mentioned would be to ring someone up and convince them to disclose their cookie. Check out[1] in which the victim disclosed their cookie without the attacker even asking for it.