Can't set user session with Vue and Django

Question

I have the Vue app and the Django rest framework api separately. One on localhost:8080 (vue app) and the rest api on localhost:8000.

So, I created an APIView that is supposed to log the user in when they make a post request:

class LoginUserAPIView(APIView):
    permission_classes = () # login should be accessed by anyone, no restrictions.
    def post(self, request, format=None):
        username = request.data['username']
        password = request.data['password']

        user = authenticate(username=username, password=password)

        if user is not None:
            login(request, user)
            user = UserSerializer(user)
            return Response({'success': 'Logged in', 'user': user.data})
        return Response({'wrong': 'username or password not correct, try again'}, status=status.HTTP_401_UNAUTHORIZED)

And I was trying to get the user session from django with axios:

login() {
      this.isLoading = true;
      return axios({
        method: 'post',
        url: 'http://localhost:8000/api/login_user',
        data: {
          username: this.name,
          password: this.password
        },
        headers: {
          'Content-Type': 'application/json'
        }
      })
      .then(response => {
        this.$store.commit('loginAuth', true); // setting isAuth to true in vuex store.
        this.$store.commit('setUser', response.data.user); // to access the user object since I don't use django templates
        this.$router.push({name: 'page'}); // redirect to random test page that requires authorization so I can see if everything went fine.
      })
      .catch(err => {
        console.error(err);
        if (err.response.status == 401) {
          alert(err.response.data.wrong);
          this.isLoading = false;
        }
      })

but I was naive and I thought this would work, so when I checked the vue app for any cookies or sessions, nothing.

How could I set user session for a separate vue app?

Thanks in advance, I apologize for my lack of knowledge.