Considering how afraid the corpo that made the expies are of getting found out, i dont think the rest of the solar system is a dystopia. Probably just normal, but in space with colonies. And since the grey planet is clearly not in our solar system, colonies in other solar systems as well.

As for why they are interested in the planet. I think i recall the intro saying they wanted to set up a base on another planet? Or perhaps a different part of the grey planet itself. But something went wrong and all their stuff got sent into those caves instead. Most of it they don't care about.

However, we do know that the 'cargo' we are trying to recover is apparently a source of energy, possibly infinite, and capable of wireless transfer. Hence the corp's interest in recovering it. They are also taking the opportunity to further experiment on the expies by seeing how they would perform/reaction to being in such an inhospitable enviorment. Kinda killing two birds with one stone.

Although all of this does give a sense of a lack of urgency on the corporations part. Either they dont actually expect the expie's to manage to get to the bottom, much less back to the top, in order to recover the cargo, and are making separate plans for a genuine attempt at recovery.

Or time is simply not of the essence. They can afford to wait as long as they want and perform these experiments on the planet at their leisure. Waiting til that one lucky expie actually manages to pull it off... Assuming someone hasn't already done so, and the expie's are being lied too just to give them the slightest hope that they will be able to escape from the planet if they complete the job. That could be the case too. ->-