Produce, used as a noun, stands for fresh, unprocessed fruit and vegetables. In a produce aisle of a supermarket, we thus expect to find tomatoes, cucumbers, and apples, but not ketchup, tinned beans, or chocolate. Produce, used as a verb, however, stands for the process of transforming raw materials into something else; ketchup, tinned beans, and chocolate, are all things that have been produced by human beings. They are artificial things, unlike produce (noun), which is something natural.
How did the meaning of the noun produce end up being limited to the things that involve the least amount of producing, much less than goes into things that are not called produce?
(The puzzling nature of the connection between the verb and the noun is illustrated by this question which shows that a nonnative speaker who has fully mastered the use of produce as verb cannot be expected to derive from it the meaning that it has as a noun; one needs to learn the latter separately, as one would learn the meaning of an unrelated word.)