Your fingerprint is not a key, it's an identity. So your design tells every place you sign in this way "I'm joering2". And if course if any of them want to log in somewhere else, they now know to say the same thing, "I'm joering2".

I guess this is slightly easier than typing your email address? But it's not a security feature.

The FIDO/U2F design is a cryptographic key enshrined as a physical key, so rather than "I'm joering2" it says: "I can prove I'm this particular key talking to your site again using mathematics".

Which key? No way to know, but it's the same one as before. Google can't use the credentials it presents to them to get into Facebook and vice versa, the proof from yesterday is worthless today and so on.