Why is normal force due to gravity regarded as contact force?

This question seems to be easy but it’s answer is related to one of deepest mysteries of Quantum Mechanics . To answer this question let’s ask a more fundamental question. What does it mean “to touch” or what is a contact? Well this questions doesn’t make sense at macroscopic scale . Let’s try to understand it at microscopic scale – The Quantum world.So for making a contact the atoms of two object should get closer and closer and closer and the electromagnetic force will oppose that but even after that something is still on the way- Pauli Exclusion principle . This principle was formulated by Austrian physicist Wolfgang Pauli in 1925 initially for electrons but later extended to all fermions. Fermion is a category of elementary particles. The name fermion was coined by English theoretical physicist Paul Dirac from the surname of Italian physicist Enrico Fermi.So now we know Electron is a type of fermion. Let’s look at the general statement of this principle which states that no two identical fermion particles can be in the same quantum state. To make electrons in contact their quantum states in an orbital has to be same which is a direct violation of pauli’s exclusion principle. The electrons as well as protons and neutrons that make up ordinary matter cannot get close enough together to allow this to happen, especially under ordinary circumstances. Now the question is what prevents contact. Is it EM force or PEP. This is a very debatable topic even for high level Solid State Physicists so we are not going to dive deep into that but now we have enough information to ans our original question . The cause of all the contact forces are Electromagnetism( or in a sense PEP ) . Contact forces are not fundamental in nature they are a part of one of the four fundamental forces of nature.