I can well imagine that this is not a semi-detached house made of two halves, but a two-family house in the form of a semi-detached house on one plot. Most likely, there would be a continuous foundation slab and a continuous roof truss, and the joint in the two-shell "party wall" would practically have no function.
Basically, even the tiniest sound bridge is effective, and pipes, for example, are often underestimated. But even the smallest mortar lumps "work wonders." Nothing simply belongs in the party wall joint (between the party walls themselves) or an elastic seal at the façade edges of this joint. According to the drawing, I suspect that this joint is limited to the facing layer and that the ETICS behind it is continuous – this would also be an excellent conductor. A foil between the halves would, in my opinion, not be the villain. If, conversely, nothing from your half is heard in the "neighboring house," the floating screed might only be poorly executed in the other half. As an owner, I would get an expert (who could verify any of my speculations, of course not by remote diagnosis), but as a tenant, moving out would seem the easiest way. However: it will not be your fault, i.e., the landlord will have the same problem with every new tenant and therefore an interest in fixing the defects.