Word for an object's "desire"

Solution 1:

The usual word for this in the computer trade is an affordance:-

A visual clue to the function of an object.

See also here.

Solution 2:

Disposition or susceptibility might be appropriate in a human context, but for door handles I’d suggest writing the sentence in a different way. For example,

If a door has one handle which is a flat surface and another handle which is a bar then, the bar will normally suggest pulling and the flat surface will normally suggest pushing.

Invite and prompt are possible alternatives to suggest.

Solution 3:

Other words that could be used here are proclivity and propensity.

Proclivity:

natural or habitual inclination or tendency; propensity; predisposition: a proclivity to meticulousness.

Propensity:

a natural inclination or tendency: a propensity to drink too much.

Solution 4:

I'd use "penchant" (noun. a strong inclination, taste, or liking for something: a penchant for outdoor sports.) or "affinity" (noun 1. a natural liking for or attraction to a person, thing, idea, etc. 2. a person, thing, idea, etc., for which such a natural liking or attraction is felt.).