I am pragmatically inclined:
1. If the rental property is considered for personal use: terminate rental contracts, renovate the property, use it yourself. It may take a few years, but it is still cheaper than a new build including land acquisition.
2. If that is not possible or not desired and the property is debt-free or lightly encumbered: mortgage the property or use it as additional capital in the financing of an external property.
You can casually inquire at the building authority for fun about their stance on a change/extension of the development plan [B-Plan]. If you’re lucky, the city planners already have the idea themselves - if you’re unlucky, they will immediately block you. But then you know where you stand and how high the hurdle is for back building.
If I assess this correctly from here and the building authority has not already earmarked the area for densification, then you will face opposition from the building authority and all neighbors to realize at best a 5-meter-wide house.
Then the question is how persistent you are. I would say it will take you at least 5 years until the building permit. If you get one at all … just the amendment of the development plan (if the building authority and neighbors cooperate) will cost you several thousand euros. So lots of money, lots of time – and in the end, at best a very narrow plot. There are other ways ... see above.
Best regards
Dirk Grafe