Welcome to the Wefugees Community and thank you for your question.
I am not an expert on student residence permits, but I can not think of a reason why you shouldn’t be able to make a PhD in another EU country. As you also left Germany voluntarily (without i.e. being deported), you won’t have a re-entry ban to the EU/Schengen area either.
As you mentioned correctly, the common asylum system in Europe is based on regulations like the Dublin law - but this doesn’t apply for study visa.
To be sure, I will also link our expert dear @mbeon-Christine here. Maybe she can add some details or correct me if needed.
In any case, please don’t hesitate to get back to us with any further questions.
All the best,