It seems to me you have a holding tank instead of a septic tank.
A septic tank receives sewage, let the solid waste settle into the bottom of the tank, and let brown water flow out on top and seep into surrounding subsoil. A septic tank usually has no power, and requires pumping every 2-3 years because the solid waste decomposes in the tank. Septic tank only overflows when the intake is larger than seepage of the brown water. It has nothing to do with electricity.
A holding tank receives sewage, merely holding it, and it requires frequent pumping because water does not seep out.
In your case, I think you have a holding tank. Your basement is below city sewage line, sewage collect in the holding tank, and requires electric pump to lift-pump into the city sewage line. When electricity fails, your holding tank overflows because water had nowhere to go.
Regardless what kind of tank it is, usually the presence of hazadous waste storage tank (oil, sewage, chemical etc) on a property must be disclosed (check your state law for confirmation). You might have a case here to seek some damage. Please consult a local attorney.
