"how can you tell a supernatural claim apart from a natural one?”
The requirement or assumption of magic.
“When a guy says to you: "That magician made a rabbit suddenly appear in his hat. HE REALLY DID!"
This is a supernatural claim.....”
No. If it’s a magician’s act, this is just an admission that they don’t know how the trick was done.
Now, the ‘guy’ might claim that ‘this proves Satan,’ which is a supernatural entity, thus a supernatural claim.
“or is it?”
No.
“With today's modern atheism, this is no longer a supernatural claim.”
Dude, it’s not my atheism, it’s having done magician tricks a few times and knowing that ‘sleight of hand’ is far more likely than magic. Even if i believed in actual magic, i doubt anyone with that power is working three shows a day in Vegas.
“FOr things can pop into existence for no reason at all!”
That’s also not atheism, it’s physics.
Nature abhors a total vacuum, so virtual particles are a thing.
“ It is perfectly "natural" for water to change into wine,”
Not if it’s presented as proof that a rabbi has magical powers.
“or a ghost to appear suddenly.”
No, ghosts are supernatural.
“There is an "undiscovered" natural law that allows matter and energy to just suddenly start existing in and of itself.”
You need to reread Hawking.
“ha ha ha. Amazing religion, for amazing faith.”
You don’t understand it well enough to mock it.
“Thus, the supernatural claims of atheism.”
None of this is atheism.