Several concepts are tangled up in your question.
The electrons in their orbitals are a stable solution to a potential problem, the potential supplied by the charges in the problem. The orbitals describe the probability of finding the electron in a position (x,y,z) around the nucleus.
How can one see the electron orbital? In this link you can see that it is not a simple matter, but it has been done, by disturbing the electron with photons and getting statistically the original location.
Once one has seen/measured the electron's location the solution of the potential no longer holds for this free electron. The probability of finding it can be described by a traveling plane wave, until it is caught by another potential and radiates down to a ground state or an energy level that was empty in an ionized atom.
Actually atoms get incident by electromagnetic radiation at every instant, if we assume electrons to get superposed by electromagnetic wave, electron can't exist as stationary wave, but according to schrodinger model, electron is said to exist as stationary wave.
A photon hitting a bound ( probability standing wave) electron can expel it from the atom . A photon of appropriate energy can kick it up to a higher energy level , the photon disappears and the electron falls back to ground state by emitting that special spectral line. It is true that atoms, and this means the electron cloud about the nucleus, are continuously hit and interacting with photons, but the grand majority of photons do not have enough energy even to ionise the atoms, let alone free the electron.
The photons in our environment are bounded in energy to first order by the black body radiation of the earth and by the spectrum from the sun which supplies the energy to the surface of the earth. The high tail from the sun which can ionize atoms and thus is dangerous is mostly cut off by the atmosphere, our shelters and clothes.
So the only two outcomes on atoms from the "superposition" you imagine are either change of energy level and disappearance of photon, or ionization of atom and change in energy of photon. This last does destroy the standing wave probability function of the electron to a plane wave one.
A free electron hit by a photon can either scatter elastically or inelastically, but a free electron is no longer described by a probability standing wave, just by a plane wave propagating ( again , a probability wave), which is also a solution of Schrodinger's equation in the absence of a potential.
That a particle decays into other particles is completely disjoint from it having substructure/being fundamental or composite.
Some examples: A highly energetic photon may "decay" into an electron and a positron in the presence of another object that takes the excess momentum. That doesn't mean a photon is a composite of electron and positron. A free neutron decays into a proton, an electron and an electron anti-neutrino with an average lifetime of 10 minutes, yet it is a composite state of three quarks.
Being constituted of other particles means being a bound state of these particles. Quantum field theoretic processes have no problem turning one kind of particles into other kinds of particles (subject to certain rules, of course), but this sort of process does not imply that the results actually constituted the input. In no meaningful way is a photon a bound state of electron and positron, in no meaningful way is a neutron a bound state of proton and electron, and in no meaningful way is a muon a bound state of an electron and neutrinos.
Best Answer
Elementary particles are understood today as the quanta of quantum fields. The fields are ontologically primary and exist even when there are no particles, but a quantum field is not “a wave-only model” as is, say, a classical electromagnetic field.
Instead, a quantum field is a continuous field, existing everywhere in spacetime, of operators that create and destroy quanta with particle-like properties. Quantum fields are not just waves, nor just particles, but rather a mathematical hybrid for which our classical environment gives us no intuition. Fortunately, mathematics makes them understandable to some degree and we find that models using quantum fields, such as the Standard Model, are extremely accurate.
One single quantum field, extending throughout the universe, can explain all electrons and positrons. (Why are all electrons identical? Because they are quanta of the same field!) One more field can explain all photons. One more can explain all up quarks and antiquarks, etc. A mere seventeen quantum fields, interacting with each other, make up the current Standard Model and are the basis for the world we see, except for gravity.