In CP victorious world, the German navy can use the AuH ports of Trieste, Pola, Split, Cattaro at alii, the Albanian ports of Durres and Vlora, the Bulgarian port of Alexandropolis, all the Ottoman ports in the Levante. This should suffice for the HSF Mediterranian patrol.
But again, Germany's strategic problem is not the Med, it's the North Sea, and the entity blocking egress from the "wet triangle" is Great Britain. So, any navy that deserves its name should invest some thought how to overcome the obstacle. As Britain can not be sunk, it has to be occupied in the next war. And if that isn't possible, it has to be isolated and besieged.