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You're right about it being an active system, but we see sump pumps required to run regularly in basements all over the place. I think these days it's just a noted fact of life with building complex structures. The reliability and operational cost is very good these days.The other solution is to allow water to seep into the tunnel (relieving the pressure from groundwater by letting it flow freely - there isn't that much water coming in every hour, so it would be more of a trickle than a flow) and then just pumping it out. The Opera house in Oslo uses this technique to stay in place, there are chambers below the basement where water flows in and is continuously pumped out. But that's an "active" and quite expensive solution.
That would be my bet for how they've solved it - seems like the simplest option (for the groundwater levels and buoyancy issues you identify).