Last I heard you have to choose an arbitrary zero point. In school you say "on the ground" is zero potential energy. But if you dig a hole in the ground that something can fall into, you can redefine the zero to be the bottom of the hole, or go to negative potential energies.
It doesn't actually matter, because like most potentials you only calculate measurable quantities using the difference between two potentials, or the gradient, or something that is unaffected by where your arbitrary zero point is.
For atomic electrons I think they choose zero to be infinitely far away, that way bound electrons always have negative potential energies. But it doesn't matter because you only ever subtract the potential energies at different places.
It's meaningless to say "I have xJ of gravitational potential energy".
I would agree with all of that;
In particular, I am glad you pointed out that;
"The choice of zero point doesn't actually matter, because like most potentials you only calculate measurable quantities using the difference between two potentials." and;
"It's meaningless to say "I have x Joules of gravitational potential energy".
