If you use
show number of unread items: Now using pinboard-API, it’s better, faster, nicer. But you have to login first.
So Safari will ask you to login to api.pinboard.in – like this (that’s the German version):
Enter your pinboard.in login, password and click “Save to keychain”.
This only happens once (if you click “save to keychain”).
Of course: Your personal data is only being transmitted to pinboard.in – the extension doesn’t have any access.