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More precisely, it's the eigenvalue (not the eigenstate) that is interpreted as the energy. When physicists say "superposition of energies", they of course really mean superposition of Hamiltonian eigenstates with different eigenvalues.When the system is described as a superposition of two or more eigenstates of a hamiltonian (operator corresponding to the total energy of the studied system).

Can this eigenstates be interpreted as an energy of the studied system?

Technically, Hamiltonian is an observable, energy is an eigenvalue of this observable.Energy is an observable, not a state, isn't it?