I think it is open loop since the wells and reinjection well...

I think it is open loop since the wells and reinjection well boreholes don't connect in the underground.
But you are right about the turbines
And apparently, even these systems have a need to deal with CO2 or other gas solved in the hot brine water that can clock up in the pipe and reduce the efficacy of the heat exchanger. I haven't found any good source about the technical details, but in some cases releasing a small amount of gas by venting is part of the strategic to mitigate this risk.

As my last comment on this topic:
the Industry-leading Life Cycle Assessment results from VUL
https://v-er.eu/app/uploads/2023/11/LCA.pdf

"Vulcan’s negative CO2 emission intensity is a product of the significantimpact offset generated by renewable geothermal energy production aswell as use of geothermal heat to drive lithium processing, and Vulcan’sindustry-leading move to strictly exclude fossil fuels as an energy sourcefrom its planned operations."

The graph on p2 shows how we get to negative missions.