What is this?
Most of these are just boxes with a small power supply to make the led work. They'll consume around 2-3 watts to light up a 0.01 watt led.
There's two kinds of power, active power and reactive power, you can read more about it here: https://en.wikipedia.org/wiki/AC_power
Your electrical company measures both reactive power and active (real) power and in most countries you're only paying for active (real) power, and pretty much everywhere home consumers only pay for real power. (there's some islands and places where electricity is produced mostly by burning diesel and coal where you may be billed for some reactive power if you're abusing the system)
In theory, the way these products would save power is by having big capacitors inside to do a sort of power factor correction, and this would help reduce REACTIVE power - the power you're NOT billed for. But the capacitors that would fit inside such box would only be good enough for something like 25-50 watts worth of power consumption at most.
So technically, it's true that they can reduce power, but it's really small amount of power saved (like I said, really small, like 1% of the reactive power your house may consume) and you're not even paying for that in the first place.
So not only your power company doesn't bill you for that reactive power, but it's not a big enough device to be actually of any use, and also pretty much any device you have that consumes more than around 75 watts is required by EU laws to have some kind of power factor correction (to reduce that reactive power).
Your computer's power supply with Active PFC for example, will have a power factor of over 0.95 (1 being 100%) while a cheap 2-3$ phone charger may have a power factor as low as 0.6

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