Has anyone done an analysis of how these laws are defining "data center"? Anyone accidentally ban having a rack of servers on an office closet? That could suck for a lot of small businesses. I'm all for local autonomy, but knee jerk local laws can also be... messy.

Laws are public, you are welcome to go read them. All of the ones I've read define it based on [x] megawatt of compute or similar. None of them are banning a rack of servers in a closet.

In Ohio: 25 megawatts. $2 million/month in electricity, call it $750m of hardware, plus the building.

This is not going to affect small businesses.

I would be surprised if a rack of servers in an office closet could realistically draw 25 megawatts of energy, which is generally the cutoff that these local ordinances use to define a "data center". Keeping in mind that the cost of commercial electricity alone for powering even a 1 megawatt data center continuously for 1 month would have to be at least 100,000 dollars, right?

I haven't seen a broad analysis, but every specific one I've looked into accounted for your concern and defined some sort of minimum size or power draw.

They never do that in the "first round". Usually you gotta wait for a compliance industry to spring up and then they inevitably lobby for the definition of people who need to pay the compliance industry to get watered down. It's just the natural incentive creep of the system.