was able to help me out.
The reason for the behavior that only the first image of each section was displayed in fullsize, was that, the first image was part of the site’s menu – and there I hadn’t activated any downscaling yet. So it was my mistake.
However, Chrome did handle the image downloading differently than Firefox and Safari. Both of them were downloading the fullsize for the menu and the srcset-downscaled inside each section, while Chrome only took the higher resolution.
Thanks @pamtbaau for the help again.