Varies on the project. As someone dealing with this locally, it varies how the project got approved. Almost all the approval is at local level, sometimes at state level. Feds getting involve is pretty rare.

A) Sometimes, it's existing datacenter that repurposed from "normal" datacenter to AI datacenter with power consumption skyrocketing. There generally is not a ton of approval in this case or power company came by asking for additional infrastructure approval and who the hell denies that.

B) Some areas classed datacenters as "industrial" use so they could be built without a ton of preapproval. Most counties have closed that loophole but existing permits may allow additional datacenters to be built.

C) Local officials approving things over desire of the voters. Alot of people don't pay attention to their local politicians despite them having most impact on their day-to-day life. Therefore, you end up with local politicians who will believe whatever they are told along with just plain overall corruption. Most of it legal.

Also, as someone who used to live in Capital Region, National Politics can suck out all oxygen in the room so local officials are even less likely monitored.

The industrial use also often comes with fantastically low rates as well.

Virginia finally started saying folks using >25MW need to pay something more than the incredibly cheap rates they had been given. But generally data centers have often gottem marked as industrial, and it's been incredibly fantastically advantageous to do so.