[ProDigit]

Though the question began and answer.
How will you propel the electric supercharger?
If it is from a turbine and generator at the exhaust,this system proves less efficient than a regular turbo; as the turbo is mechanical in nature, and there are no losses from outline to input shaft.

If it's driven from a battery, a normal engine wouldn't make nearly enough electrical power, to power this. The power drain on an engine is greater than with a belt driven supercharger, as again, the belt driven supercharger losses are negligible compared to a kinetic to electric, back to kinetic system.

The electrical power a regular car can provide, is only enough for powering a high flow blower. This blower, has the capacity to raise a HP or two at low rpm, but it is an actual restriction at the higher rpm, where you need the power.

From the video, it was clear that not even 2x 120V 1000+W leaf blowers, provided enough airflow for a small car at peak RPM.

So electric superchargers, we're talking about high voltage applications.
240+V batteries need to be installed. They will be able to provide power for a faction of minutes to an hour, before the batteries need to be recharged, or replaced. And after which, the engine will run outside of it's compression ratio (low ratio).
Exhaust scavenging is a delicate business, that has to be done right.
In case of lots of acceleration and braking, you are better off running E15, or E85, or 89,91,93 octane gasoline, and bump up the compression ratio on a slightly larger engine.
In case of occasional acceleration, mostly cruising, a regular turbo on a smaller engine would be more efficient.
A supercharger rarely is efficient, only to the point of bumping up compression to the needed 11:1 ratio or so.
You're much better off getting a larger size engine, than a small one with a supercharger.
Unless again, you can enable/disable the supercharger boost depending on driving condition. Then it won't be any different from a turbo, and still a costly installation...

In case you already have a too small engine, nothing beats the simplicity of a belt driven supercharger, for low initial cost, but also lower MPG, or a higher initial cost of a turbo/intercooler system, with possible added mpg over time.

If you had the means, and could install a small ev battery in the trunk or so, and a motor to one of the rear wheels, however small it may be, and could program it to provide acceleration at a given pedal position, but disabled itself at higher (than 45mph) speeds,
You could possibly improve city acceleration by much, at the cost of a little less hwy mpg.

If you'd enable the motor even at hwy speeds, the battery capacity needs to be increased by a lot.

An electric motor as helper assist, makes most sense on small cars.