About €1000 for oiled beech with continuous lamellae.
I was just downstairs on the ground floor to measure, since we actually have it somewhat like in the picture, only 3m wide. However, we executed it differently than planned, for the reasons mentioned here, although we initially liked this picture and the idea. I am a fan of things that make life more beautiful, but I always check—or have checked—whether it actually "improves" my life.
Your open space is about 40 sqm, if I see that correctly. The windows in the current plan are set centrally in the wall, so this wooden slat, with the currently drawn 45cm, will protrude almost 30cm into the room. Not only does this cost you about 0.6 sqm of living space, it also intrudes disruptively into the room and you will bump into it more often than you will sit on it. Not that I don’t understand your wife’s wish, but the benefit versus disadvantage does not match. You will have to plan and economize carefully with limited space for furniture and movement, as you don’t have much room for frills. Our windows are flush with the outside of the brickwork, so more of it disappears into the wall, yet we had it executed with only 34cm as a nice, wide windowsill, i.e., a window seat, without anyone actually sitting on it. 40 cm is hardly more; try it out and on one side you need a cold, straight wall. You will sit uncomfortably in every respect and deprive yourself of possibilities in the room. Maybe you should build your house first and then, when the house is standing, use a template made of boards to see how the whole thing really feels and especially when the kitchen is built, because it obviously depends on it as well.
In our case, visitors or children can sit there—it has never been used for sitting, but it is nice just for decoration or a generous view outside.
By the way, I wouldn’t like the door right next to it; I would prefer if the window were directly in line of sight from the front door, to look outside when entering the house—that I like very much, for example.
I would first ask myself whether dark, oiled beech fits with my other interior design or maybe a different wood, but especially whether this €1,000 wouldn’t be better spent as a down payment for a really permanently and technically sensible controlled residential ventilation system. Otherwise, I would explain to my wife that she is 100% responsible for ventilating all rooms several times daily for the next 30 years.