Hi @Jannis, welcome and thank you for your question! I have changed your post’s title to bring it in line with the question guidelines and make it easier to understand from the title:
Good titles are questions you would ask your friend about Typst.
The way citations are displayed depends on the bibliography style, and there are styles that use footnotes, such as chicago-notes. In Typst, you’d customize the format by changing/providing your own CSL file. If you don’t want to do that, maybe Pergamon can help you implementing what you want.