I just finishes looking through the quest and could not find anything that would forcible changed the class in the Arachne Story. The ceremonial blade also has a listing id. So I am not quite sure what caused this.
Yes, the weapon class needs to be changed at the shop in town. Equipping any weapon not matching in the right class will result in no usable skills. That's how it should work.
The game saves your equipped weapon before any transformation happens. And returns it to you after changing back into human form. But it does not change the class you are having selected.
So maybe your saved weapon id was outdated and at the end of the quest the game gave you the previously saved weapon? That's the best I could come up with.