How can you study the properties of something you don't believe exists?

Edit: People are downvoting this, but I genuinely want to know how "theology is the study of supernatural things" and "theology does not rely on belief in the supernatural" are not in complete contradiction.

Religious faith from certain perspectives is something like: choosing to believe despite being unable to comprehend with your rational mind. That's the basic core of the inquiry, you start from there and see what happens.

Choosing to believe without evidence is antithetical to the core of inquiry.

"Choosing to believe" in the supernatural is the opposite of "theology does not require belief" in the supernatural.

You've stumbled upon one of the most profound spiritual questions there is.

How is that a spiritual question? More skeptical.

No, that is religious studies. Theologians all believe in god or other supernatural entities.

There's debate on the terminology, so I'll credit your first point. But there are atheists who also study theology. https://en.wikipedia.org/wiki/Hector_Avalos is one such example.