Welcome back to the Wefugees Community and thank you for reaching out to us.
I am afraid that the "Einbürgerungsamt" (naturalization office) and the "Standesamt" (registry office) will not "share" your birth certificate copies and the translartions - but this is only an assumption. I hope you still hold the original birth certificate? I would recommend you to contact the naturalization office directly in order to have a concrete overview regarding the requirements and the documents they request for the process.
In any case, please also don't hesitate to keep us updated here or to get back to us with any further questions.
All the best,