So I'm reading a manga and this girl is giving a guy two pieces of paper. She says "正直者ですね。両方セットで差し上げます。” I would think that a を particle would be used here since the set of papers is an object. "I give the set of papers (to you)." What do I give? The set of papers. I'm looking here, https://core6000.neocities.org/dojg/ , at the 4 main uses of で and none of them seem to explain the particle's usage here. Can anyone explain what で is doing here.
Because she omitted the part of the sentence. For example if she was giving apple(りんご)...
... is the correct way. "りんごをセットを" sounds weird. The example you have shown omitted the part "りんごを". That's the reason she says "セットで". In the web site you have shown, I believe で(2) is the closest usage.
By the way, you can also say ...
So just saying "セットを差し上げます" is correct too.