You previously asked about self-employment with Aufenthaltsgestattung. In that case I answered that it is possible with the permission of the Ausländerbehörde. I based that information on the following document which gives a good overview of access to employment and self-employment in Germany for different types of residence papers and permits:
The document is only in German but on page 25 it covers Aufenthaltsgestattung. Under the column 'Zugang zur Selbständigkeit' (acess to self-employment) it says it is possible with the permission of the Ausländerbehörde.
However, I have now researched this question further and found other documents with the information that it is not at all possible with Aufenthaltsgestattung. For example at the very end of this document from the IHK:
However, neither source provides a specific legal basis I could check. Ultimately you will get an answer if you apply for permission from the Ausländerbehörde to do the freelance work you mention. Send a written application along with examples of the kind of freelance jobs you are offered.