Puglia or Sicily?

If it helps, Lufthansa flies non-stop Munich to Palermo, last time I looked.

We spent a little more than two weeks in Sicily and could have used more time. I would cancel Praiano and add those days to what you are thinking of for Sicily. You will be happier with this plan.
Or spend that larger amount of time in Puglia. We loved our ten days in Polignano a Mare. Rent a car in both destinations. We combined these two destinations, flew from Bari to Palermo on Volotea. Fabulous experiences!

Puglia would be more relaxing. There are many interesting towns, including the coastal towns and Lecce.. There are flights from Bari to Munich.

I'm another one who believes Sicily needs more time (and Puglia as well, for that matter). My husband and I made two trips to Sicily (basically one for the east side and one for the west) for a total of five weeks. We still didn't cover everything we would like to have seen. We were doing it by public transportation, however, which adds time.

If you had one or two destinations in mind for Sicily, it need not be too much more time-consuming: private transfer to Naples, flight to Palermo or Catania (I would not do the ferrry with such a short time frame). But I would also save Sicily for a larger chunk of time and I think it would be much easier to rent a car in Salerno and drive around a bit of Puglia. Drop car in Brindisi or Bari, which should both have flights to Munich. I've flown to Bari on Lufthansa twice.