Actually bedrooms have numbers too ... and in the exact same style.
I think that's my main issue. All rooms have a symbol, albeit on the opposite corner, but it's non-interactive (clicking it is the same as clicking the room). You can hover over it and something info pop ups. But if you hover over the number nothing happens. And there's just no indication that this specifically is a button. Buttons in the game typically have that glossy black background ... so this at least should have that too.
And possible a mouseover tool tip.
Anyway. You don't need to explain the button to me; I get it. But that doesn't mean the UI can't be improved.