I worked in a small DC (I think it had about 10k servers at its peak). The only time there was noise outside was if the generators were running due to an extended power outage or maintenance. We had a few trailer generators that were added on as capacity increased. Where I worked was right on the other side of the wall to one of the computer rooms and I don’t recall hearing anything. It only got loud when the door was physically opened to walk in the room, that noise was mostly from fans.
I also toured one of our larger data centers, and even inside the small cube farm area it felt like a normal office. The noise only picked up once inside the room with the servers.
Noise during construction would probably be worse than noise during operation.
Part of the stop-gap plan of the White House is for DCs to run those backup generators at peak hours. That would be for years until the new power plants get online.
Anecdata, but I was once on a tour of a colocation DC. Located in Vegas, near the old town in a basement of some office building. Completely unassuming from the outside. Inside it was a little loud, but not terribly so. Busy street level noise maybe.
