What could this scammy "magic whole-house electronic powersaving surge protector box" have actually done?
The red disks are MOVs (metal oxide varistors); these are the "surge protection" aspect of the device. There are four groups of them, for line-to-neutral and line-to-ground for both lines.

The small silver tubes are fuses that are intended to blow in order to prevent a fire when the MOVs fail, since they often fail shorted.

The large silver cylinder is a multi-section electrolytic capacitor, which is connected line-to-line. It is either a nonpolarized device, or the multiple polarized sections have been connected in such a way as to effectively make it nonpolarized. It is notionally there for "power factor correction", but this a waste of effort in a domestic application.

It looks like the big capacitor is also being used to drop the voltage (limit the current) to the indicator lamp, which is probably neon.