The supernatural can exist only in the supernatural world or another worlds that's separate from the natural world, one of which is our imagination.

Only 'one of which'?

Yes, only one of which. Because obviously it is possible for the theoretical supernatural worlds to exist beyond our imagination due to unlimited iteration of possibilities AND impossibilities that can exist. Think about it this way, if the supernatural world is not bound by the natural law, the rules of cause & effect, then that world can be anything, everything and nothing. Chaos! Since we live in the natural world, our minds won't be able to truly perceive the endless iteration of chaos.

Simply put, theoretical supernatural worlds can exist without anyone having ever thought about it. Also, there is a difference between concept & form. Just because we might understand the concept of a chaotic world, it does not mean we can perceive every single iteration of these lawless worlds.

On another note, I have something to say about the testability of God.

As long as God can cause change in the physical world, then God can be tested. Even if God lives in a world where natural laws are different, the key to the answer is the bridge between the 2 worlds. For this bridge to exist, it needs to operate on laws consistent to both worlds. When there's a consistent law, then it is possible to devise an overarching law to explain both worlds, like how we explain dimensions with different laws of physics.

So, if theists says that God can cause miracles, then he God is testable. However, to prove that the so-called miracle is caused by God, theists need to prove that gods exist first through other means, otherwise, they'll just be committing circular reasoning.

One last thing I want to comment on before I finish.

What is the difference between an extremely powerful wizard and God? We are led to believe that we owe God the debt of creation, so God is supposed to be like a father to us. That's why when atheists insult God, theists get their panties in a twist. But before they get angry, they should get the proverbial paternity test first by proving God's existence.