The regularity of the electrons' behaviour in atoms has the same ontological status as the regularity of the characteristics of electrons and said atoms.
I don't have a clue what this means.
But if there is an electron it is following a set of "rules".
That is how it is known as an electron.
These regularities are understood as characteristic of reality.
The "rules" are what leads to the characteristics. Things don't just have characteristics for no reason.
Just like things don't just have structure. There must be "rules" to define scope and limit to have any structure.
To have objects made of atoms there must be "rules" to define first the atoms and then the ability of the atoms to bond together to form what to our eye appears as a 3D object.
...Yet, if nature is regular...
Nothing is just "regular".
To have regularity many conditions need to be met. Like, there must be structure of some kind to have regularity.