So, I uninstalled the game completly, and downloaded/ installed it completly new. After that, I can set the trap. Still dont know, what the problem was, besides probably an missing file on my end, after an update... but now, it works. Not only with an New Game +, but also with my old save.
yes I normally manually update files by copying the new folder into the old one and overwriting the old files. It's the first time, this hasn't worked.