Cladding bathtubs, with a skirt or built-in masonry?

Troubleshooting takes precedence over symptom treatment :)
Those who plan well don't need solutions ;)

Too late, because the house is already built.

I am more concerned about the type of covering, which material would be recommended.

Drywall or Ytong or otherwise masonry. Alternatively, a plastic apron.
Then tiles or plaster or plastic panels.

All materials you can imagine are suitable for this non-visible area. But you do need a proper transition to the part that stands against the actual wall.
Is the tub placed directly against the wall or is there a tiled shelf area? What is the installation situation? How is the splash guard and waterproofing ensured against the window so that no water runs down there? Etc.

So your question is answered. Unfortunately, you can't really make use of the answer because it doesn't just depend on the material, but also on the overall situation.

Is a freestanding bathtub still possible? Even if it is very close to the window or the wall, from my point of view that would be the nicest solution.

I am currently reading about prefabricated houses. I missed that.

Walling in or skirt - both are technically sound solutions. The choice depends on how you want to integrate the bathtub into the room and how the rest should be designed. In addition, the appearance of the skirt and the bathtub is unclear. Technically, you can’t go wrong much; I would rely entirely on the visual design and your own taste (and maybe a bit on the budget). The situation is as it is now; criticism would only make you unhappy. Since the window, connection, and drain are apparently fixed, I would look for a bathtub model that fits the room so as not to place the corner in front of the window. There are great freestanding solutions, and there should be space for them as well.