> Looking at the other signage along Bahnhofstrasse, I think one might be supposed to go on the sidewalk, but not on the street?

No, there would need to be a blue pedestrian sign with a white "Velos gestattet" subsign on the footpath for this to be the case. Otherwise the law is that all footpaths within 2m of a road are strictly for pedestrians, and bikes should ride on the road. For paths further away from the road or not parallel to a road, they are usually signed as roads with motor traffic banned, in which case bikes are allowed; or as roads with all traffic banned, in which case they aren't.