In my opinion, singular "Quelle veste apportons nous" should be allowed. This is because, the speaker could also be asking his colleagues which of the many vests that they use at work, they are supposed to bring. The colleagues will understand the question in the singular mode. In which case, it is very singular. Thus, both answers should be added to the answer repository.
You are correct. English jacket has sleeves and English vest does not have sleeves. But you are wrong when you say French veste is a vest. French veste is an English jacket.
Veste is a false friend. It looks so much like the English vest that you think it is. The word looks like the word in the target language. It often sounds the same or very close. But it isn't.
A better term is false cognate. False friend is misleading because they actually are your friends if you trying to learn a language.
In all the confusion of thousands of words to be added to vocabulary, there are some that are pretty easy. One group is true cognates. They look the same, they sound the same and they mean the same thing. False cognates are another group of words that look the same, sound the same which makes them very easy to recognize but have a different meaning than the expected one.
They have an added benefit sometimes as well. In this case Duo has introduced you to the idea that veste is a jacket. This will help you remember that manteau is not. It is heavier and longer than a jacket. If the jacket is a dress jacket you might put a manteau over top of your veste to protect it and/or yourself from unpleasant weather.
One strategy when learning a language is to focus on the articles/prepositions etc. Then learn all the true cognates. After that look at all the easy to recognize false cognates. Working from French or German to English that way will provide a surprisingly large amount of commonly used language in a comparatively short time.