It would generally be the opposite, what law gives them standing to sue?

My knowledge as a non-lawyer generally agrees with above, most states won’t allow you to sue for neighbors doing something legal that decreases your property value (CA is the exception I’m aware of, and even then it’s a “sometimes” kind of thing).

I’m not even sure who they’d sue. Presuming the land is zoned for a datacenter, the datacenter is allowed to do datacenter things. You could sue the city to try to prevent the zoning, but sovereign immunity would preclude suing them for doing their job (zoning, in this case).