This hasn't happened yet in New Mexico with a data center because these are new. But it has happened numerous times with other capital-rich entities that have bought water rights (sometimes, just cities buying rights from adjacent rural county land).
A small community near where I live no longer has functioning wells because new residential construction below them sucked the water out of the aquifer. They tried to drill deeper, without much success. County is now having to build a water line to the community.
Reminds me of a quote from some otherwise forgettable movie I saw: "My father left me with very little, except for all his money."
For the record, my net worth increased by about $1M before taxes based on the 1 year of options I got at amzn. But not relevant in this context.