Fermi energy is the maximum energy that particles have when total energy of system is in the ground state. Fermions cannot occupy the same state. Electron is fermion. In the case, there are two states with the same energy due to the two spin components of electron. Each two electron have the same energy level.
Fermi energy is highest energy.
We should find the next possible lowest energy state of total system. That is the system where only one electron is excited to and the state of the rest of electrons is not changed. Bosons can occupy the same state. Ground state energy is The first state is the state where only one electron is excited to the next level .