I just realized something huge.
>!Hades is incredibly fond of you and interested in you because you are his late friend's sundered form.
As was Ardbert.
The help with the Lightwardens? Wanted to test your power and coax you into joining him to get his friend back.
The invitation to Amaurot? He wanted you to be there with him. He didn't register you. I believe that by idealizing his friend as a citizen, he also saw you as one, so the Bureau recognized you as a guest of honor.
His friend's sentience? He was thinking of both him and you, knowing you'd realize Amaurot was an illusion, which projected said knowledge unto his friend.