Comment by cardanome
No, that case would be fine if the side business would be being self-employed. No one cares how many hours you work if you are self-employed. (Mostly, I am simplifying here)
What is an issue is working employed for two jobs and going over the 48 hour limits.
Working that much is very unhealthy so the state needs to protect people from being exploited. People should be able to live from working full time. Having to work multiple jobs and to destroy your own health is morally abhorrent.
Under German law being employed by a company and being self-employed are legally very distinct things. If you are employed you get protection from being fired, you have to have health care, pay into the retirement fond and so on.
If you are self-employed you are on your own. You can decide if you use public or private health care, you need to figure out how to save up for retirement yourself and so own. You get more freedom but less protection. That is because the law realizes that working people need protection from exploitation but also wants to give freedom to those that want to try their own business.