In addition to what @Eric said, I want to point out the use of state. From your example, it is apparent that you are just counting natural numbers, therefore you should use counter instead. Also, the .update() method, if the function is passed, expects a new value, but you provided none. For state this will therefore set the new value to none, for counter this will give an error.
Here is what you should use instead:
#let c = counter("test")
#let fun(id) = [#c.step()#label(id)]
#fun("test")
#pagebreak()
#link(label("test"))[link]
#context c.get().first()
Although this still looks somewhat strange to do without additional context/information.