The FIDO U2F and WebAuthN standards explicitly address this issue, because it is a valid concern. No, your key cannot be detected as being the same key on website A and B.

Undoubtedly the same holds true for these Microsoft services.

What Freak_NL said. No, there is no globally correlatable identity, and it won't be possible to either create or authenticate credentials silently. Browsers will show confirmation popups and YubiKeys will start blinking to prompt for touch confirmation.