Terraced house on a 240 sqm plot - fundamental questions / feasible?

however, when we talk about a chain house here, we mean a closed design

Unfortunately not. A chain house is neither fish nor fowl, but §22 (4) of the Land Use Ordinance. The development plan overrides the usual mechanisms of the State Building Code (in BW §5 (1) sentence 3) and must describe exactly what is intended. And if the city planners have worked sloppily here, e.g. through missing, ambiguous, or open-to-interpretation formulations, conflicts with the building authority naturally arise. But since many houses are already standing, I am surprised that these conflicts are still unresolved.

If it helps, attached is an excerpt from our development plan:

Building method (§ 9 (1) 2 Building Code in conjunction with § 22 Land Use Ordinance)
According to the entries in the site plan, the building method is designated as the "Open Building Method" pursuant to § 22 (2) Land Use Ordinance and a "Deviating Building Method" in accordance with § 22 Para. 4 Land Use Ordinance.
a) In the case of the "Deviating Building Method 1" (A1), the residential buildings are connected to each other via laterally attached garages or ancillary rooms ("Terraced house construction method 1"). With the exception of the building on the southernmost plot, the residential buildings on the southern property boundary are to be constructed as boundary buildings and must maintain a minimum distance of 5.00 m from the northern property boundary. The distance between the residential building and the northern property boundary is to be closed by intermediate buildings, which may contain, in addition to garages permitted in the distance area, ancillary rooms or living rooms. The intermediate buildings are to be provided with flat roofs. The depth of the intermediate buildings may not exceed 9.00 m, the maximum building height must not exceed 3.00 m with reference to the determination of the ground floor floor height (single-family house) of the structures shown in the site plan.

The distance between the residential building and the northern property boundary is to be closed with infill buildings, [...] The infill buildings are to be provided with flat roofs. The depth of the infill buildings must not exceed 9.00 m, the maximum building height must not exceed 3.00 m with reference to the specification of the ground floor slab height (single-family house) of the structures in the site plan.

Aha. So here building height (instead of the otherwise usual wall height) is a maximum of 3.00 m, also not averaged over natural terrain, but with reference to the height datum point; and valid for the entire infill building (so a terrace could not start 3 m away from the boundary on top). Flat without anything - no cream, no chocolate sprinkles, no powdered sugar :-(

...Intermediate buildings are to be fitted with flat roofs...

The characteristic of a flat roof - being walkable - is not excluded. It remains a flat roof after all.

...the maximum building height must not exceed 3.00 m ...

If no SUV is to be parked in the garage, I think you can still incorporate a parapet / attic within the 3m above the finished floor level and still have 80 cm parapet height on the walkable flat roof.

Discuss with the planner, provide floor-to-ceiling windows as access, design the garage roof as low as possible (clear room height for example only 1.80 m) with corresponding load-bearing capacity - walkable. An attic that fully utilizes the 3 m. Do not explicitly designate it as a terrace in the building notice/application.

The characteristic of a flat roof - being walkable - is not excluded. It remains a flat roof.

That is correct so far. However, a few months ago - I don't have a link at hand right now - we already discussed the topic where the consequence of the fall protection* opposed the terrace desire. Here we still have the trump card regarding the height definition, possibly lowering the garage (which, however, entails drainage effort). Is there really so much luck involved in being able to look at the neighbor’s plate from above? *) If I remember correctly, the original poster there (unfortunately without prospect) hoped for leniency if the parapet was transparent

The need for such a terrace can already be significant with a total plot size of only 240m². But how to best approach this now... no idea. The above is just an idea of mine, no idea if that makes sense.