The water at these temperature / depths has a lot of dissolved salts and minerals so it's not (human / ag) usable. Modern designs are closed loop systems where production wells bringing the hot water to the surface go through a heat exchanger to a different working fluid to drive the turbine and then is re-injected back into the reservoir. There is consumptive water use for fracking the reservoirs in these types of enhanced geothermal systems, but beyond that it's more water redistribution in the area around the well systems where re-injection and production lead to different pressurization from pumping / natural ground water replenishment rates.

> One of the problems with the data center boom is its use of fresh water. How does geo-thermal plants use water and how much?

Baring leaks, ground source heat pump geo will consume no water at all. Water is pumped from one layer of the aquifer and is returned to a slightly higher layer.

I dont know why this keeps coming up? It is a closed loop system. The water aren't used at all.