Hi @Adeeeloua
The only difference I see that having a valid Greek residence permit makes is to do with the visa process. If you wish to receive a student residence permit, you will have to withdraw your asylum claim. You will then be told to leave Germany and apply for a student visa. As you have valid residency in Greece, you can go and apply for the visa at the German embassy there.
In addition, for a student residence permit you will have to show you have enough money to cover your living costs during your studies. If you remain in the asylum process and study, then you can generally continue to receive asylum seekers benefits. This, however, is at the discretion of the Sozialamt.
Best,
Éanna