Does that mean exactly one thousand apples, or over a thousand apples, or roughly a thousand apples, or up to a thousand apples?
Of the choices you gave, "over a thousand apples" is closest.
exactly one thousand: no, because if it was exactly one thousand you wouldn't need the 上 to denote upwards at all
over a thousand: closest. 上 conveys above, when used with hundreds or thousands, typically used to convey the sense of abundance and excess of hundreds or thousands
roughly a thousand: no, for same reason as #1
up to a thousand: no, because if it were up to, it would be something else like jihu/nearly
In the magnitude of thousands. If I see descriptions like this, they usually exaggerate a bit for the effect, so my understanding would be more like "oh, its up to 1000, maybe in the 800-900 ballpark."
Edit: Ok 上千 literally means "the figure can reach thousand". But again, such expression are more commonly used to emphasize the magnitude, so expect exaggerations.