Okay, it seems that Photoshop has problems with alpha channels and .tgas. I did not experience this bug in the 15+ years I use PS now.
However, this has nothing to do with my problem, because then I would see a big fat black border around the window or I should be able to see the buttons entirely (depending if the alpha channel is just approximated to pure black or pure white).
Also, how does that correlate with me not being able to resize windows in the lower right corner, for example, where I did not change anything?
The same behaviour occurs when I save my design as png and import it. Yes, this workflow eliminates the alpha channel error, but it does not in any way correspond to my problems.
The two things why I bought WindowBlinds are a dark background in the file explorer and less distracting window frames. So please dont tell me that its not possible to just alpha out more of the top bar? The image behind it should not affect the behaviour. The dimensions are the same. If it would look ugly, okay, my fault, but this makes windows unusable...