The website should display a qr code you can scan with your phone that allows you to then login, unfortunately a lot of sites don't implement this, and some don't implement backup codes. This isn't the fault of passkeys per se, but of poor implementations.
That's still a terrible solution. Plenty of people don't have phones that can do that, or dont have e it with them when they do etc..
How does scanning the barcode with your phone log you into the computer? Does your phone need network access for that?