It did no such thing. The evolutionist faithful are simply indulging in further wishful thinking by asserting as much. A single court decision does not have the capacity to determine what is or is not science. Even by common use of language it does not make sense to call a tangible, directly observable process (intelligent design) "unscientific", let along "religious" or "supernatural." Science itself cannot objectively determine what is or is not supernatural. Do you really think "expert testimony" will sort it out for us all?
In fact, Judge Jones in Dover wrote that whatever his personal biases might be, he had no choice under the rule of deference to previous decisons and to the SC.
You are pursuing a losing line of argument here.
You have a big time logical inconsistency here. Let's say for the moment that via experiment and observation and inference (your terms) that there comes about a scientific finding of a supernatural event. This would be very powerful. There would be an experiment or observation that was repeatable, that via objective reality, all who looked at the evidence could agree on it.
The job of science is to describe how the natural world actually works. The unnatural is not part of science. By definition, this "supernatural effect" becomes a description of the natural.
The result is that God is dethroned. Any mystery is now reduced to being an effect that can be examined in a laboratory, measured, and known. So evidence for a "supernatural" influence actually destroys the supernatural by making it part of the natural, verifiable, measureable part of existence.