I read that is was $10,000 a pound when NASA began launching the shuttles in the 90s.
I used a number from a private company. Also, I’m not sure if the 10k number, which is what I recalled from when I was dealing with NASA, is low or medium. Low Earth orbit still has some atmospheric drag, so you have to launch fuel with it to keep it in a stable orbit.
Having dealt with NASA, they often charged more to do a study than a private company charged to do the actual job.
The reason you see mining mentioned in so many science fiction stories is there is damned little reason to go to anyplace but Earth. In the starting narration of just about every movie now “the Earth was devastated by Global Warming and wiped clean of mineral wealth.” They have to say something because there’s literally no reason to leave Earth. Imagine what a day would be like on a moon base, or on Mars. No sunshine, no walking outside, no plants except indoors. Boring, boring, boring. The suicide rate would be through the roof. And if you have a crazy neighbor, you’d be forced to kill him.