One more update from me:
So far, nothing has changed. The installation spacing of the wall heating is still at 10cm and the site manager wanted an on-site meeting with the heating engineer, site manager, and the general contractor’s boss. I already had a bad feeling about that.
They did everything to make me dislike the 5cm installation spacing.
But what it was actually about is the warranty for cracks. The 5cm wall heating will now be installed, but the issue of cracking is causing headaches for the general contractor. The deal now is that they will do everything possible and, if necessary, embed reinforcing mesh in the plaster to prevent cracks. However, I will sign that I release them from the warranty for the 3sqm in case of cracking.
Then the floor heating installation was discussed in general. Unfortunately, fully installing the floor heating in the shower will not work. The screed will only be done up to about half of the shower by the screed layer, and the rest by the tiler due to the necessary slope for the drain and the partition wall at the end.
I have reluctantly extracted from the site manager that a "Schlenk" floor heating will be installed in the shower as well and that they will pull the screed as far into the shower as possible.
I believe my general contractor has learned a lot about floor heating, flow temperature, installation spacing, and also persistent clients from our build. My wife is very annoyed every time I discuss the topic, but we are paying for the party and have to live with it for the coming decades.