Covalent bonds are EM (electrostatic/electronegativity) or not? This is not a duplicate, I am not asking why covalent bonds form or how they form. I am asking whether the covalent bond itself can or cannot be classified as a EM interaction (or if it is caused by a EM interaction)
I have read these questions:
How does covalent bonding actually work?
What makes the difference between ionic and covalent bonds?
Explanation of covalent bond from physics point of view?
Where Ben Crowell says in a comment:


It doesn't create any electrical interaction. In a covalent bond, each atom is still neutral.


What gives covalent bond its strength?
Where Gert says:


To the right is also schematised the electron probability density ψ2 and note that this density is very significant on the nuclear axis, between both nuclei. This causes the intra-nuclear Coulombic repulsion force to greatly reduce and the molecular arrangement to be stable, meaning that pulling it apart would cost energy.


What makes the difference between ionic and covalent bonds?
Where Manishearth says:


For covalent bonds, we have something known as electronegativity.


Now one says it has nothing to do with EM interactions, and the other ones say it is due to electronegativity, and the fact that intra-nuclear Coulombic repulsion forces greatly reduce when a covalent bond (a common molecular orbital) is formed. 
This is a contradiction, both cannot be right. Covalent bonds must have a real reason to form and this can or cannot be electromagnetic, electrostatic, or be because of electronegativity. Or it could just be a non-electromagnetic cause, like a QM phenomenon. Anyway, there has to be a clear answer whether covalent bonds are classified as (and caused by) EM interactions or not.
Question:


*

*Are covalent bonds classified as EM interactions or electrostatic interactions or a effect of electronegativity?

*Or are they just a QM phenomenon that we cannot classify (and explain) in terms of electromagnetics?
 A: Covalent bonds are unequivocally due to the electromagnetic interaction. The electrostatic interaction is just an approximation in which the dynamics of the (quantum) electromagnetic field are neglected, and sometimes that approximation is good enough. For studying the static or quasi-static properties of covalent bonds, it's usually good enough.
In the simplest model, we can treat each nucleus as a stable elementary quantum particle, treat the electrons as quantum fermions, and consider only the electrostatic interactions between all of these particles. Schematically, the Hamiltonian for the quantum system looks like
$$
 H\sim \sum_j\frac{\nabla_j^2}{2m_j} 
  + \sum_{j\neq k}\frac{q_j q_k}{|x_j-x_k|}
\tag{1}
$$
where the subscripts label different species of nuclei or different electrons, and the last term (schematically) represents the Coulomb interaction. The wavefunction must be completely antisymmetric with respect to permutations of the electrons' coordinates (Pauli exclusion principle).
This model, which neglects magnetic effects and radiation, is often a good enough approximation for the purposes of calculating the static (non-dynamic) properties of atoms and molecules. It fails to capture chemical reactions in which the ability to emit or absorb electromagnetic radiation is essential. For those effects, a quantum treatment of the dynamical electromagnetic field is essential. The model also fails to capture some subtle static effects for which magnetism/spin is essential.
This is consistent with all of the quoted comments, when fair allowance is made for the different specific things that those comments were trying to emphasize. For example, the comment "doesn't create any electrical interaction" isn't meant to say that the bond is unrelated to EM; it is only meant to say that covalent bonds don't rely on having an unequal distribution of charge among the atoms (say, among the two nitrogen atoms in a nitrogen molecule). The whole idea of "atoms" is a little ambiguous in the case of covalently-bonded molecules, because the nuclei are sharing electrons with each other. 
Regarding the specific questions:

  
*
  
*Are covalent bonds classified as EM interactions or electrostatic interactions or a effect of electronegativity?
  

Electrostatic interactions are just EM interactions in which the magnetic contribution is neglected. As stated above, for the purposes of calculating static (non-dynamic) properties of atoms and molecules, the electrostatic approximation is often good enough. "Electronegativity" is just a name that describes a particular electrostatic property. 


  
*Or are they just a QM phenomenon that we cannot classify (and explain) in terms of electromagnetics?
  

I'm not sure exactly what is being asked here, but maybe this will help: In situations where the dynamics of the electromagnetic field is important (such as situations involving emission/absorption of radiation), it must be treated as a quantum field in order for the model to be self-consistent. For some purposes, such as calculating the static properties of covalent bonds, the electrostatic approximation is often sufficient, as in the model represented by (1). In that model, the only dynamic entities are the electrons and nuclei, so we can say that covalent bonding is an electrostatic effect. However, although the Coulomb interaction in that model is not mediated by any dynamical field, that model can be derived from QED in which the Coulomb interaction arises as an effect of the quantum electromagnetic field. 
