So it's one thing to imagine you're a programmer who does a small amount of contracting on the side; now imagine you're a teacher who does some "mild" sex work (say, solo camming): the social and financial repercussions on them having their second job disclosed is a real risk. Even from the employer's point-of-view, it's a risk to their reputation for hiring such a person (there again, such a thing seems unlikely to be considered good enough reason to dismiss someone outside of their probationary period in Norway).

So how exactly would they find out how you earn that money? And why would they have the right to terminate you if it's not in the original contract?

Most businesses paying a salary expect (and sometimes encode in your employment contract) that it is your sole job. They don't want the stress, mental fatigue, and time commitments of a second job competing with your work for them.

(This is my understanding, as a person living in the US anyway.)

If you look from it from an employers standpoint, that employee might not be around for much longer if his/hers side-business kicks off. It can be hard to find candidates that can replace that employee.

If the employee makes more money from that business than from yours, the employee has literally nothing to lose and may start to become sloppy with their work, not take it as seriously as he/she should, etc.

I'd say it's all about control.