Well, if by "Application State" you mean:
Application State (also known as Program State) represents the totality of everything necessary to keep your application running. When we refer to application state we are normally referring to the state of the program as it exists in the contents of its memory.
What is State and Why Does it Matter? - thedaylightstudio.com
Then for the most part you'll find your Application State is not on your diagram. It's over here where the Entities live:
That being said, every layer holds some state. Even if it's mostly just configuration info.
However, some applications go out of their way to eliminate "Application State". They're called stateless.= They push all responsibility for knowing things onto the DB. That way the application doesn't change from request to request. Makes it easy to know if it's in a good state since it only has one.