I know that there are scattering experiments that show that electrons act like structureless particles up to extremely small scales. But in these experiments the electrons are moving, so their wave function cannot actually be considered point-like in the sense of a $\delta$ distribution.
Usually, if I imagine an electron, I think about a coulomb potential reaching up to but excluding $r\to 0$. Of course, as we all know, if the corresponding wave function was really shaped like $\delta$, this can only be an instantaneous event due to quantum mechanics and the completely undefined momentum in this case. So in the next moment, the single electron's wave function would already have dispersed to some extent, but this is not the focus of my question.
What I ask is, are there any experiments at all, where the electron's wave function reduces to a $\delta$ shape, and where we can check somehow that its coulomb potential is as nice as we imagine it? If we make a double slit diffraction experiment, the electron will only be localized to the size of the atom that captures it on the screen behind a double slit. If we get a single $-1e$ charged ion into a trap, it is the same situation.
Shouldn't electroweak interaction and the Higgs mechanism that gives the electron it's mass, give it also a structure on very small scales? I think if the electron was strictly Coulomb shaped, it was also strictly electromagnetic, and so there would not be the possibility for weak interaction, right? Or is this a too simple mental picture?