Cladding the gap between semi-detached houses - What is the best way?

Ok, then I withdraw my professionally unqualified objection.

It is precisely the solid connection that makes a semi-detached house what it is. We have already lived in 2 different ones and never had problems with noise to the neighbor. I still don’t understand the purpose behind the gap if a semi-detached house was desired.

For about 40 years, semi-detached houses have been built almost exclusively with multi-layer building separating walls with separation joints; these run all around, i.e. roof, exterior walls, floor slab, foundations.
A semi-detached house may look like one building from the outside, but the load-bearing structures are actually almost always strictly separated, with a distance of more than 50 mm.
The absence of this separation joint affects the quality of sound insulation. It is not uncommon for owners of semi-detached or terraced houses to have the halves subsequently separated with a diamond wire or diamond chain saw if the planning and/or execution of the separation joint was inadequate.

A semi-detached house may outwardly look like one building, but the load-bearing structures are actually always strictly separated, distance > 50mm.

That's exactly what I mean! The distance is not visible from the outside. And that is probably what the OP is getting at.

That's exactly what I mean!

Your "filling expansion joints" I - probably mistakenly - interpreted as completely filling the expansion joint through the entire building depth. A technically correct, superficially optical masking of the joint is usually done using permanently elastic rails, mushroom head profiles, or a permanently elastic, sprayable joint compound. Mushroom head profile is out due to the building offset, and it is also important to pay attention to the possibly necessary ventilation.

Yes, I was unclear there. I understood the suggestions mentioned by the OP "Lüftungsgitter" and "Lochblech" to mean that they should remain visible in the end.

Ask a plumber. I would make sure to get something reasonable at that point.

What the construction manager suggests, sticking sheet metal over it, is okay. Use PU adhesive as glue. Brand name Sikaflex. If the joint were a bit narrower, you could fill it with pure Sika. That also holds. But for me, it’s a bit too wide here. Karsten