My feeling is that putting a "discourse marker" in a lesson mainly about prepositions and pronouns is bit.... well.... inefficient?
Well, it seems to be used as both discourse marker or in a literal spatial sense. Duo accepted "next to that" so it's nice to see that it also has a meaning of "besides/futhermore" and you can have a kind of light bulb moment about the etymology of both the English and the Dutch words.
"Furthermore" is an adverb meaning "in addition" or "moreover". My Dutch/English dictionary translates "furthermore" as "bovendien", and "bovendien" as "besides, moreover". I believe "bovendien" is the intended translation in this sentence, not "daarnaast".
"Beside" and "besides" do not mean the same thing. Most commonly, "beside" is used to mean "next to" or "alongside of", translated in Dutch as "daarnaast", while "besides" is used to mean "as well as, furthermore, other than, etc.", or the Dutch word "bovendien".
I wasn't familiar with "daarenboven" but now I see that it too means "besides".
When I look at and read the Dutch sentence out loud, the word "Daarnaast" (literally, there next to) to me indicates a location. For example, say you're on a crowded bus or train and you see just one empty seat that you really want to take, but the person in the seat right next to it doesn't look too inviting, you might think to yourself "Daarnaast ga ik niet!" or in English "I'm not going next to that (there)!"
I find that the English translation of the Dutch sentence, "Besides, I'm not going!," doesn't make any sense in this case. A better way of saying that in Dutch would be "Trouwens, ik ga niet! I suppose you could use "Daarnaast" to mean 'Besides" if you changed the word order a bit and put in a comma: "Daarnaast, ik ga niet!" although it still sounds a bit strange.
Hi! native speaker here... daarnaast, in your example can be used, but you won't see it very often. It depends on the context of the writing before that. For example: De modellen worden geselecteerd op uiterlijke kenmerken. Daarnaast, het karakter is niet belangrijk. It would be better to write: Daarnaast is het karakter niet belangrijk.