Re: Liquid cooling
The cooling system itself uses electricity to move the heat away from where you don't want it. Usually it does this by pushing the coolant (air, water) around. More efficient cooling systems use less electricity to move a given amount of heat. That's where the touted energy savings are coming from.
The stuff OVHCloud are talking about doing here is passively cooled, so they're able to get very close to zero energy being used by the cooling system. Hence the claimed PUE almost equal to 1. It's really impressive because normally it's hard to get passive cooling to scale up to moving lots of heat.
In a PC, in theory a liquid cooling system may use less electricity than just fans because the liquid system moves heat from the CPU to the radiator very efficiently, and then moving heat from the radiator to the environment is much cheaper than moving heat directly from the CPU to the environment would've been. The radiator is easier to cool than the CPU because it has a much bigger surface area. Also the radiator tends to maintain a fairly uniform temperature too because it's made of metal and full of circulating water. If you want to bring the electricity cost of cooling down even further, I've heard of DIYers using huge radiators which are so big they can be passively cooled. I remember reading once about someone going to a scrapyard and picking up a car radiator.