[theohuber]

Thanks for your replies @noggin and @wrxtasy 
Meanwhile I've found the solution: the Sony TV requires HDR enabled at two points: for the entire TV (General screen settings - advanced image settings, as mentioned by noggin) and once for each HDMI Input (screen/image settings).
Now Kodi plays the 4K HDR movies with correct colors. If I go to the image settings of the sony TVs shield HDMI input while playing HDR content, the small "HDR" sign appears too :-)
Thanks a lot for you help!