What does Erwerbstätigkeit nicht gestattet mean?
Erwerbstätigkeit nicht gestattet / Erwerbstätigkeit nicht erlaubt means you are not allowed to work - both self-employment or employment are forbidden. This is usually mentioned on your visa (tourist / schengen) which allows you to visit Germany but not work.
In order to work, you must apply at the Ausländerbehörde and get a residence permit that allows you to work; this can be a Blue Card, Freelance Visa, Job seeker visa, etc. You need explicit approval from the Ausländerbehörde.
Your residence permit must say
Erwerbstätigkeit gestattet allows both self employment and employment
Beschäftigung gestattet in which case you can do employment but not self-employment.