So, after our plumber told us that we can indeed install a surface-mounted fitting on the exterior wall and we finally got to see the bathroom in the model house again, we changed our minds once more.
The bathroom will be like the last idea in the first post, but without the suggested door opening. The two walls and the opening will be ceiling-high.
Thus, another room within a room is virtually created, the shower will be larger, 140 instead of 125 cm deep, and we can install a pre-wall between the shower and the bedroom so that the pipes are not in the wall and you’re not live in the bedroom every time someone showers.