What happens if I choose to copy an empowered unit when I equip an unempowered unit with Shady Spectacles?

Being empowered is a status and is not copyable, thus the equipped unit will remain unempowered.

Shady Spectacles applies a copy effect to the equipped unit. Copy effects copy the printed (or copied, if another copy effect has already been applied) traits of the unit being copied. Empowered is a status, a temporary modification, and not part of the printed traits of the card, so it will not be copied by Shady Spectacles. Whatever temporary modifications are applied to the unit as the copy effect is executed on that unit will be unaffected by the copy effect. If the unit has Might increases or decreases, a buff, the empowered status, Temporary, attacker, defender, etc those will remain in place.