Strange:
Ok, they were missing the money for the finished bathroom, as far as I'm concerned, but wouldn’t it have been possible to tackle the elimination of the moist biotope in the basement at some point? Are there any traces of failed repair attempts?
The realtor admits: there is a relationship "groundwater --> water level in the pool," which is why it is now lower than before. As soon as the water level rises, for example due to a neighboring future construction site, water will flow freely through the basement again.
Relationship to precipitation rather unlikely, you have to water if it is very dry for a long time. Nevertheless, there was obviously water in the pool.
Photo 1 shows what I would say is a water ingress point in the masonry to the left of the radiator in the corner.
The realtor suspects the lamp openings, but are these really open at the back, so sand can get in there? Where would the sand come from there? If yes, that would be easy to solve, but I don’t believe that. Instead, I suspect the pile foundation at different heights: some piles support the pool, some the higher basement floor. Already during construction the piles outside under the walls sank by a few millimeters, but those under the pool shell did not, as they were unloaded. The pool shell basically stands too high and has therefore separated from the rest of the foundation; water is now entering through the cracks. Warning: pure speculation
Edit: I find the idea of a 5x6m swimming pool in the basement pretty cool! If somehow possible and financially justifiable, I would have it completed and please never fill it in!