Trying to read up on some physics on my own, I have a basic understanding of physics and inorganic chemistry. What is actually the Fermi level at a conceptual level? I see different definitions for it: one explanation says that at 0 K, it is the highest possible energy state for an electron of the system. In that case, why is the Fermi level in pic related not located at the very top of the valence band, which is where the most energetic electrons of the system are at 0 K?

Also, why would it located in the middle of the band gap, isn't that technically a forbidden energy?

On the wikipedia page, the Fermi level is defined as the work needed to add an electron to the system, can that be related to the explanation I gave above?

Thanks for answers