What does the bonus item from completing the Darker Side do?

This answer contains spoilers.

1. The Invisible Hat makes you invisible, except for your shadow. This has the side effect of making the game harder to play. It's more difficult to dodge attacks or land on Cappy when you can't see Mario's body. Enemies do not behave differently; they act as if they can still see you.
2. When you approach a friendly NPC when wearing The Invisible Hat, they will say "???".

Reference for #1:

Reference for #2: