You sums are wronger than a wrong thing.
You completely neglect the fact that the Moon's reflected light is beamed out over a very wide angle, covering a far greater area than a complete hemisphere of the Earth. The mirror would be focussed to an angle of far less than 1 degree, designed to illuminate only a tiny fraction of the Earth's surface (so requiring many orders of magnitude less light than the Moon to do so).
Comparison with a telescope mirror is comparing apples to elephants. Telescope mirrors must be rigid to keep a precise shape, and so are thick & heavy. An illuminating mirror would not need to hold a precise shape, and would be made of extremely thin and light flexible sheets that are unfurled when in position.