People have done a lot of work in the field of "geothermal energy" and there's a fair amount written about it.
If I wanted to actually put in the effort for this, would I be armchair engineering here?
Why do you have to exhaust the steam? Isn't piping that back into the cold instream a more efficient option?
Just pointing out that a turbine lowered into the borehole would need to have a low pressure side so there would be a pressure differential. You can certainly use incoming cool water to condense the steam to make a pressure differential. In doing so you create hot water which you can cycle back into the heat source preheated. However, keeping the water in a closed cycle means there is no need for incoming cold water for cooling. Somehow something has to escape from the borehole or you end up with a static system, so you would have to pump out the warmer condensed water.
Check out power plant descriptions and you'll see that there is always a movement of heat through the system. Some of the heat energy is converted to mechanical energy but some is removed at the condenser either via moving river water through or more often passing condenser cooling water through a cooling tower.
They really did a lot of work with this in the '60s and there are geothermal plants operating in a number of places where there is volcanic activity bringing heat close enough to the surface for it to be practical. There are probably some good online resources on what has been done and some ideas for increasing use in the future. (It's been years since I studied this but IIRC there was an issue with the exhaust containing some undesirable chemicals picked up from the volcanic activity and ground water percolating through igneous rock.)
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