First, you do not need to $unwind to $lookup as it is smart enough to lookup each element.
Since you want the result to be in instructions you might as well use it as the as of the lookup. The your $unset was on the right track to remove the lookup artifact. But I would opt for $map because I could specify all the fields I want rather than having to know which fields I do not want.
Lookup at this playground.
Next time you publish documents with _id, please make sure the _id is value. It is a pain to cut-n-paste in order to experiment with your data. With what you shared we get: