Other definitions of supernatural really fail to be complete or useful. One definition is 'not predictable' , but by that metric, every moment of a newborns first few moments of life is supernatural.
Of course, there's another definition, which is experiences that do not take place in this world and unobservable to us. In which case, sure but then we cannot experience them here on earth. The moment such a thing is experienced by a human, it becomes natural
I honestly challenge people to explain what they mean when they say 'supernatural'.
There’s a physical realm we exist in defined by space and time. Everything outside of that is the supernatural.
God is not bound by time and His true nature is not something we can fully understand. He is in our world, but not from it.
The Bible makes references to angels and demons, entities that cannot be seen or measured unless they choose to make themselves known. They can affect still affect the natural world. These effects can be observed, but it would be difficult to reproduce any experiments because they are an unknown variable.
Science has trouble differentiating between an effect without a cause (a miracle basically) and an effect with a mechanism we haven’t accounted for.
Why not both?
Everyone agrees that brain chemistry-stuff happens when you have a supernatural experience, just as brain chemistry-stuff happens when you eat a steak. The disagreement is whether that's all that's happening. Pointing to the existence of brain chemistry-stuff as an argument against the existence of the supernatural is like pointing to it as an argument against the existence of the steak.
Also, the 'supernatural' does not defy physics or logic; it is perfectly logical, and outside the scope of physics.
In other words, even if you assume that the vision of God/feeling of divine presence/etc. is valid, there are two methods of implementation: either it’s done in a supernatural way that defies physics and logic; or it’s done in a way that accords with the structure of reality (as in, chemically.)
The latter seems a lot more elegant to me, IMO.