Can I fly to Taiwan and for sure get a 72 hour transit visa to enter Shanghai again to pick up my luggage?

Hi I am a German passport holder currently staying in Shanghai with a prolonged student X (which expired on July 31st but which I could prolong as a 停留one) until August 31st which is when my return flight to Germany leaves.
I would like to visit Taiwan before I leave mainland but want to leave my huge travel suitcase with a friend in Shanghai.