Nice to hear from you again.
In order to get a visa to enter Germany, you have to have a valid passport or another document that is valid for purposes of identification ("Passersatz" or "Ausweisersatz"). The underlying law is AufenthG §3 (https://dejure.org/gesetze/AufenthG/3.html).
In accordance with AufenthG §48 (2) a residence title which contains information about its owner and a photo, is sufficient to work as a substitute for a passport (https://dejure.org/gesetze/AufenthG/48.html).
To me it looks like you can either use your home country's passport or the document that has been issued by the Italian government (if it fulfils the criteria mentioned above).