Is there a word for a button that is not being held?

Hello Ocelot welcome to EL&U. There are at least three terms which are used in slightly different circumstances. However none of them is used often because a button which is not pressed is in its default or natural state, there would have to be a good reason for referring to it at all. The three terms I can think of are:

Unpressed This is probably the least uncommon. It could be used in narratives. A novel, for example, could have a passage like He reached towards the bell but the young man said 'My mother was Jane Smith'. The button remained unpressed (I apologise for the trashy style)

Unactivated This is more likely to be used in a more technical context. A technical manual might say "The unactivated buttons are examined by the program but have no effect on its operation."

Default state This is even more technical but does cover the case of buttons which are 'normally closed' as well as the more common 'normally open' buttons. 'Normally closed' buttons complete the circuit when the are released and break it only when they are pressed, 'normally open' buttons do the opposite.

Which of these you would choose would depend on the context in which you were writing but "unpressed" is probably suitable in most cases.