If pâtisserie can be translated as "bakery" (a kind thereof), which I always thought it could, then "The bakery has no honey" needs to be accepted.
The pastry has no honey makes no sense, shouldn’t it say “the pastry has no honey in it” the pastry has no honey seems to mean that the pastry does not have a girl friend.
I'm no native speaker but it does seem strange without "in it". My version would be "The pastry doesn't contain honey".
It's not a problem for me. "The pastry has no milk, eggs or honey because it is vegan." You can use "in it" if you want, but it's optional.
Then it should probably accept both. Unfortunately, I don't remember if "in it" was accepted when I did the exercise.
It sounds perfect to me without "in it", but I am not a native speaker.
Is there a way from the sentence to determine whether this is a baked item containing no honey, or a bakery that's run out of honey to bake with?
It would have been clearer that the subject of this sentence was cakes if "les patisseries" had been used rather than the singular.