LSA's are indeed quite rare in Germany, as they are quite expensive. Flying them requires a full PPL or LAPL(A).
You first need to ascertain to which extent your lapsed Zimbabwean PPL can count towards any form of license in Germany. The Germany CAA, the Luftfahrtbundesamt, would be your port of call in this respect, I suspect.
Flying a German Ultralight requires a different license, the so-called SPL (Sport Pilot's Licence). If you have a valid - German! - PPL or LAPL(A) you can acquire one with conversion training. It's issued by any of two associations; DULV or DAeC. While German Ultralights are sold in many other countries as LSA, they do differ in one important aspect, and that's the MTOW which is limited to 472.5 kg.
Syndicates are fairly rare in Germany, flying clubs are quite widespread though.