'adj. broody, inclined to sit or incubate;

No I don't have a study on a strict definition of the word broody. The word "inclined" kind of covers it don't you think.
Inclined
you're likely to do something, you're leaning toward doing it, or you do it habitually.
Nothing about actually doing it

One wouldn't describe a mother of a newborn child as broody would one? So, why would one describe a chicken mother as such.
So, I think it's a fair split into getting prepared to do something (hatch eggs in the chickens case) and sitting, (debatable) and being a mother (task already achieved, intention carried out).
I can't see any reason to apply a different meaning to the word broody just because a chicken is the subject.
I find it's easier to delineate each stage. It helps to understand the various physical and one must assume, psychological, changes the hen undergoes.
The behaviour of a broody hen and a sitting hen is rather different. There's that inconvenient trance state when sitting which we understand very little about.
Broodiness starts long before one sees the puffed up hen I would suggest. It's just that many humans have difficulty accepting that a hen, or any chicken come to that, is capable of planning.