Thank you for reaching out to us again and for contributing to our interactive platform with your question.
I understand why you are confused about your situation and there have been a few cases on our platform where people were asked to acquire a passport from their "home country".
As the following website explains, people who have subsidiary protection like you are obligated to take part in the acquisition of their passport/ papers stating their identity. For people who received a positive BAMF decision, receiving a residence permit mustn't depend on the submission of the "home country" passport. Also: if the acquisition of said passport is "unreasonable" (unzumutbar), you receive replacement papers for your ID (according to §48 Abs. 4 AufenthG).
The exact words in German:
Subsidiär Schutzberechtigte sowie Personen, bei denen Abschiebungsverbote vorliegen sind zwar verpflichtet, an der Beschaffung von Identitätspapieren aus dem Herkunftsland mitzuwirken. Die Erteilung einer Aufenthaltserlaubnis aus dem positiven BAMF-Bescheid darf aber nicht von der Vorlage eines Heimatpasses abhängig gemacht werden. Ist die Mitwirkung an der Beschaffung unzumutbar, erhalten sie Ausweisersatzpapiere (siehe § 48 Abs. 4 AufenthG).
For people how were granted asylum or refugee protection, going to the "home land" embassy to acquire a passport can even lead to the termination of their protection title. Therefore, they receive the passport for refugees.
As another source states, people with subsidiary protection usually do not have an entitlement to German documents/ passports for refugees. They are only issued in certain cases: if there is no embassy of your "home country" in Germany; if the embassy is denying to give you a passport, because of reasons you are not responsible for (e.g. your nationality); or if the acquisition would be bound to unreasonable conditions (e.g. having to pay a bribe/ putting family members in danger/ or else). This is further explained in §5 AufenthV.
Source (please use a translation program for an English version): https://www.nds-fluerat.org/leitfaden/10a-fluechtlinge-mit-aufenthaltserlaubnis-nach-25-abs-2-satz-1-alternative-2-aufenthg-subsidiaer-schutzberechtigte/10a-1-aufenthaltsrechtliche-situation/#sdfootnote6sym
If you have an unclear origin and the embassy wouldn't issue you identity papers - or acquiring your passport could put you or your family in danger (or you'd have to return...) - it should be reason enough to apply for receiving a German replacement ID.
The websites advise to reach out to a refugee council/ legal aid service for refugees to have a closer look and see whether or not you have a chance to get a refugee passport. You can tell us where you live and we can look up some contact details.
I hope this information helps. Feel free to reach out to us again if you need any further assistance!
All the best,