but with us, a new house can practically be built within the old walls.
Yes, that is a popular method that is very often used in rural areas. Legally not entirely clear, definitely complex, expensive, and complicates modern floor plan design. However, I do not see the necessity here at all. Everything here looks like unplanned inner area (§34 Building Code). A (re)development of the cleared plot is definitely possible. And possible boundary development to the west should also be undisputed. The questions are whether an extension must be attached there, whether that also applies to the east, how high the surrounding development is, what percentage of the respective plot area is built upon, how the uses look, whether factual building boundaries or even building lines can be identified.
the plot is very narrow
The plot is not narrow. It offers many possibilities. Only that an inexperienced planner does not recognize this. I am also not a design talent, so just a suggestion to overcome possible mental blocks:

Standard terraced house floor plan possible, size and creative changes dependent on budget and of course on the answers to the above questions