iPhone recognizes security key, doesn't log in

Check for and apply updates for the Yubico Authenticator app, and updates for iOS. Force-restart the iPhone. Test again.

Test the key itself, too:

• https://www.yubico.com/genuine/
• https://demo.yubico.com/

If the key is not a Yubico Yubikey and from some other hardware provider, check with their equivalent testing tools.

Then for further assistance with the Yubico Authenticator app, contact Yubico support.

Apple has integrated two-factor support available on iOS 18, which might provide an alternative path to testing or an alternative to using the Yubico Authenticator app.

Use security keys to sign in to your Apple Account on iPhone - Apple Support

Check with Yubico, as a starting point.

Particularly given the Yubico website is not working.

They’ll likely know if it’s an issue with their app, their key, or with iOS.

They may know about the related aspects of the third-party apps, as well.