How do I get through this door (and what's behind it)?
It seems the only way to get in that door is to break the Golden Rule so that the statue will move while it's trying to attack you. There is a chest in the room with 4000 denarii.
The same door seems to be pictured/outlined in the link below, detailing its location right after the tavern, to your left.
https://itemlevel.net/the-forgotten-city-how-to-get-the-treasure-behind-the-golden-statue/