Construction loan - Ex-partner does not pay his share

Declaration of division in the land register? That could still be a chance if there are 2 actually divided residential units. However, only if the bank does it as a "goodwill".
Otherwise, both ex-partners are jointly and severally liable. Stopping payments is unwise. Especially regarding one's own creditworthiness and the occupied house.
The notarized contract only has effects on the two parties who signed it. So it (probably) only concerns enforcing claims afterwards. The situation is definitely complex. Especially for laypeople like those found here. So urgent legal advice is needed.

Moreover, a bank could report to Schufa. They are initially not interested in how the "internal relationship" is.

So, I don't want to sound like a smartass, but when I think about my variable financing, which was at a similar amount and split into 2 parts, then 30k€ is just a payment of 90-120€. For me, it was 90€. To risk the bank pledging both residential units would be (I'm putting it politely) "unreasonable."

The same applies to a lawyer. What good does it do for you to be right and possibly win, if a) you don't get the value of the dispute back and b) are stuck with the litigation/court costs.

I would annoy the good lady until she continues paying on her own. There are moral means and ways to do this. You just have to get creative.

The problem, however, is that you are essentially paying for the apartment of your ex as well. You then have to get that money back. And some exes are reportedly very unreasonable in that regard, which is why I don't see it as so far-fetched.

Just out of curiosity - what about simply selling the house?

Question: Are there any joint children involved? If not, from my point of view, selling would also be the simplest solution. Clear cut.

Just out of curiosity - how about just selling the house?

you also have to initiate a forced auction. Again, costs.