So, the solution is here. For everyone who is interested:
A stainless steel chimney inside the house is fine, but in every floor above the stove, a fireproof enclosure must be created. According to the chimney sweep, this involves using drywall profiles and 2 layers of drywall at a distance of 10 cm around the chimney. And this box must, in turn, be 10 cm away from combustible parts... Ceiling openings are tightly concreted and that's it. Only on the floor where the stove is located may the pipe be visibly open.
Sounds quite simple....and cost-effective.