Yes, the vast majority are closed loop systems and the water isn't really used up, like a lot of these headlines imply.

That's not to say the energy being used can't be put to better uses, though.

Evaporative coolers save a ton of energy compared to refrigerator cycle closed loop systems. Like a swamp cooler, the hot liquid that comes from cooling the server is exposed to the atmosphere and enough evaporates off to cool the liquid by a decent percentage, then it's refrigerated before going back into the servers.

Data centre near me is using it and the fire service is used to be being called by people concerned the huge clouds of water vapor are smoke

It is a closed loop, but the paper treats it as if it's an open loop, and counts all water use for the building, as well as all the water that went into creating any equipment used.... and the water that escapes power plants in powering the buildings.... it also includes any other buildings that might house related services. Here is the original "study" which is about what maths could be done given the above assumptions:

http://arxiv.org/pdf/2304.03271

In short, it has nothing to do with reality, and is more just an attempt at the authors to get their names out there (on bad science that the media is interested in publicizing for click bait reasons).

It highly depends on every data center, but it is very likely that they do use municipal water for cooling. Mainting a Reservoir is extremely expensive for the amount of thermal mass it requires, these things kick off HEAT.

You can run a geothermal loop in reverse and use the earth as a giant heat sink.

You need something to move the heat away, like water or air. Having something solid that just absorbs will reach its heat capacity pretty quick.