Dark stain on the wall

You should definitely check the lower seal of the floor-to-ceiling window above. If there is a draft inside, it is definitely not sealed properly. If nothing is noticeable there, then check from the outside. Are there any pictures of the installation? The faulty lower seal of floor-to-ceiling window elements is unfortunately a common construction defect.

If you don't see anything at first glance, then get a thermal imaging camera and try again with it. Especially with the current temperatures, you could quickly notice a difference. A few threads above us is also an example. Many electricians also have them lying around or you can politely ask companies if they would lend one for 2-3 photos in exchange for a small donation to the coffee fund.

The suspicion is very close in the window area. Start the search there.
Best regards, Peter Schwesinger