Thank you for getting back to us with more details on your case and sorry for the wait.
Before I continue: in order to leave a comment and stay on the same thread (which makes following the conversation easier for other members), you can click on the "Comment" button below any answer! If you receive an E-Mail notifying you that you have an answer, you can simply follow the link to the thread where someone responded and comment on the answer. I hope this makes it easier in the future :-)
From what I could gather from my sources, it is usually possible to travel back to Germany legally after voluntarily returning. If you get deported, you are not allowed to enter Germany again for a few years.
However, if you have received a rejection as "obviously unfounded", then returning to your home country voluntarily doesn't change your entry conditions and in principle, you are not permitted to go back to Germany.
I hope this answers your question. Please reach out to us again if you need any further assistance!
All the best,