This is common in Germany at least in the scope of patents and inventions. That is, if you make any invention at have it patented or market it outside of your job, your employer owns that patent and the profits ("Arbeitnehmererfindungen"). Luckily, a slow beaurocratic government works sometimes in our favour, as they never updates the law to apply to software, and software is not patentable in Germany or the EU - so we can work on side projects in software without that affecting us. But if you are a mechanical engineer, you are screwed.

That's not correct. "Arbeitnehmererfindungen" only apply to inventions you make as part of your paid work. See https://de.wikipedia.org/wiki/Arbeitnehmererfindung

Whatever you do in your spare time is up to you and your employer has no saying over it, unless he can prove that it negatively impacts your job performance.