The question I have is: do you want to preserve the property? Are you attached to it? Are there emotional ties (I’m not assuming any monument protection)? Or do you just not care and want to get living space as cheaply as possible?
Do you want to move in yourself or rent it out?
If renting out, I would do a strict cost calculation: how much do I have to invest with which option, how much do I get back with which option?
If self-occupying: what is important to me? As cheap as possible or do I have specific ideas about my future house?
Personally, I would rather aim for a new build for myself and with 10m width and lots of space in length, you have good possibilities for a nice house; a lot is possible there. Being 5m away from the street would not bother me either; if necessary, you could build one or two garages in this area.
For intended rental, I would weigh options as outlined above. However, it must be considered: such an old house is a “grab bag.” You won’t get around a full renovation with basement waterproofing etc., and during such a renovation, problems often arise that were not recognizable before. This can happen even with experts. WITHOUT an expert, I would not decide anything here at all, since it’s not just the basement. Apparently, a complete heating system has to be installed, probably all sanitary installations will have to be redone, and in that process, the electrical system will also be brought up to the latest standards. Energy efficiency must be taken into account, so the building might have to be completely insulated, etc. Then room layout and requirements today are completely different from the time when both houses were built. So spatial adjustments will probably be necessary as well.
Therefore: first clarify with an expert whether renovation still makes sense given the current building fabric. No one here can do that. Even a building expert lurking around the forum couldn’t do it based on a few pictures. That would be more than unprofessional.
If you tend anyway towards a new build, then you can save yourself this step and just tear down. I don’t know how much floor space the two connected houses have together, but my parents’ house (built in 1973) has about 140 sqm of floor space and unfortunately a damp basement. Initial inquiries about the cost of waterproofing the basement resulted in a rough estimate of €80,000. And this basement does not look nearly as bad as the two pictures above; there’s no mold either. Just to give you a rough idea. So: such a renovation will definitely not be cheap, it should really pay off in the end if you want to keep the house. If there are emotional reasons for preservation as well, one might be more willing to invest in renovation.
But only you can decide that.
Either way: without an expert I wouldn’t even start...