And what about harvesting water from the sea and filtering it for data center cooling? It would lower the strain on freshwater sources and combat rising sea levels.

I don't know if that's commonly done around the world, but it's definitely a thing in at least the Google data center located in Hamina, Finland (one of thte the data centers mentioned by HoloDust earlier). Sounds like there might be some challenges with that approach, and it probably works best in cooler regions, but it definitely seems to be a viable solution at least under suitable circumstances.

Of course using sea water for cooling probably requires the data center to be located near the coast.

Oh, and dumping warm water back into a cooler area might have some undesirable effects. It's probably a very local thing, but again, pick your poison, I guess.

What about finding a more practical use for the water after it's been run through the cooling system? It could be run through a treatment facility and made drinkable.

There could certainly be applications for the water, but I don't exactly have a ton of ideas myself. It could be raised high up where it can't cause harm to cool down, but that would take energy. I guess some of the energy could be reclaimed by using the water for hydroelectric power once it's cooled down, but I'm going to guess it's just not worth it.

I'm also going to guess that your idea takes a lot of energy.