I asked you for a specific example of something we could learn "about the universe" from a source other than the application of science. You refused to give one so we are no further forward.
Music is one example.
Do you mean like expecting science to tell us whether we ought to prefer pistachio or chocolate ice cream?
Exactly.
On the other hand when theists claim that god acts in the physical world - as you have - it is entirely reasonable to turn to science to investigate those claims. That would be a proper application of science.
Even if we have a physical evidence like a medical cure for instance it's not possible to consider this physical evidence as scientific evidence because repeatability.
If someone claims to have been cured then we can scientifically investigate if such cure indeed had occurred. But we can't put a scientific evidence about the cause of such cure.
The Catholic Church for instance demands a scientific evidence about cures. The scientific evidence will only states that some improbable cure had occurred and that's it. The scientific evidence can't say if was a paranormal cure. Usually the scientific conclusion is just "no natural explanation found".
There's a very defined line when science ends and metaphysical claims can be made upon it.
Particularly I think clinical cures are rare and only occurs in a Catholic context.