"The girl, whose bag I also have, speaks very slowly."
Translation:Het meisje, wiens tas ik ook heb, spreekt heel langzaam.
No, I don't think this was intentional. I haven't seen them make grammatical errors intentionally yet. "wiens" is definitely incorrect, but a lot of Dutch people don't know that anymore - probably including the people at Duolingo. Nevertheless, "wier" is becoming obsolete fast, but rather than using "wiens" I'd suggest using "van wie".
Yes, wier can also mean seaweed, but that's not relevant in this context. And yes, wiens = whose when referring to males. However, this sentence is about "het meisje" = female, so wier would be the right word here. It's not considered a big mistake to use wiens, but in cases like this (female subject) it's generally advised to use "van wie" rather than "wiens" if you don't want to use "wier". See also https://onzetaal.nl/taaladvies/wiens-wier/
I hope this makes it more clear?
Wiens actually is the masculine form, wier being the feminine and also the plural form. More and more, however, we see wiens being used also for female subjects. This is indeed quite common in speech. But e.g. in the newspaper, wiens and wier are mostly used correctly. I agree wier is rather archaic now, but wiens is still quite commonly being used, at least in written language.