Learn English – A word to describe the next level of action

The answer to this question will depend on the syntax of the phrase into which you wish the answer to be injected.

The button has a property called pushed

make sense in programming contexts, for example, where the property's datatype would be a boolean (if the button is two-state, either on or off).

This programming example is based on the linguistic fact that the past participle ("pushed") can be used adjectivally to convey the notion of the 'state' of something.

If we abandon the syntax in your fill-in-the-blank example, we could rephrase the statement and say "The button is pushable" or "The button can be pushed".

One of the button's attributes is that it can be pushed.

Strictly speaking, (i.e. in natural language not programming terminology) "the button has a property called pushability". The word "called" wants a noun there, not a past-participle adjective reflecting state which in some circles (e.g. programming) is used like a noun. The naming conventions of programming are sometimes unnatural.

Consider to shake out. Example usages:

If you don't have time to fold a load immediately, shake out the pieces and lay them flat in the laundry basket (CNN)

Shake out clothes when you remove them from the washer. (NJ Laundromats)

Shake out clothes from wringer and drop into fresh, warm suds. (Approved Methods for Home Laundering)