While an interesting idea, I think you’ve greatly understated the problem. First, lasers and coherent light beams diverge, light cannot stay perfectly collimat

While an interesting idea, I think you’ve greatly understated the problem. First, lasers and coherent light beams diverge, light cannot stay perfectly collimated and it’s not really possible to collimate well over such long distances. So the receiver, >10,000km away, will “see” only a small cross-section of beam. The efficiency of this is defined by something called the overlap integral between the areas of the beam and the detector. Think of it like the amount of light from a flashlight that gets through a pinhole in a sheet of paper. This reduces the available signal power significantly. If you introduce mirrors you have the mirror loss plus the vignetting losses for each bounce. This is likely much worse.