Earlier quoted context omitted.
In most engineering offices I've been into being a morning person would mean you have less overlap with everyone else, since coming in late and staying late is the norm. In one company I consulted for, a morning person almost got fired when a regional manager noticed he left 2 hours earlier than everyone else. It was hilarious, in the saddest possible way.
Can confirm; I have been that morning person who left 2 hours before everyone else and, while I didn't get fired, I was punished for it.
See you tomorrow.
Oh, is it that time already?
Leaving so soon?
Bye now.
And it may not be intentional, but it comes thru that way.
The easiest way to leave is to not say anything. Just grab your things and head out, which can come across as antisocial, but it avoids the awkwardness.