So I tried doing what Ralphzoontjens initially suggested, which is finding that well-hidden first-layer setting and changing it to 0.02mm. After I had set that, I switched to layer view, and then it just worked perfectly. It has now been sliced into layers, so I can see that it also includes the bottom part of the card.

Concerning the size of it, I'm aware that the file I attatched it says that its 8.56mm x 5.4mm x 0.04mm, but I don't know why it says that. When I created the object in blender, I am absolutely sure that I set it to 85.6mm x 54mm x 0.4mm. So when I import it to cura, I just scale it up to get the right size that I want
I'm gonna try to print it out tomorrow, and see how it goes. I expect that it will probably be ultra thin and very fragile, but hopefully I can work with it
Thank you so much for your help! I'm really glad you took time to answer my questions