Thank you for the quick answers
So, iron may be the problem or missing fertilizer. I am glad that this could be spotted by @mistergreen
and @Jorge Soirse
I took the book "Planted Aquarium" by @dwalstad
and went through some of the chapters mentioning iron, nutrition and fertilizing.
One aspect I found interesting is how iron is made accessible to plants by photo-chemical reaction in the water (DOC-Fe3+ + Light -> Fe2+ + oxidized DOC).
Another aspect was that fertilizing should be done via adding fish food (shrimp food in my case).
The last interesting aspect was especially the penetration rate of iron in fish food (no matter what kind of food), which should be absolutely enough.
Diana also writes that rooted plants get their iron from the soil, which would support my observation of the rooted plants looking totally fine. I also have a Ceratophyllum floating in the water, which look pale as well, but not so much). So my guess is that you are right and it is the iron missing in the water that is not accessible to the floaters. This is supported by the fact that there are absolutely no visible algae in my aquarium and the glass is totally clear.
But the solution of adding fertilizer seems to easy to me and not appealing. The whole point for me to try Dianas approach was that I would not need such things. Of course, there is no problem in adding fertilizer to my aquarium, but is there a better, easier, and more sustainable way?
At the moment my lighting consists of a Fritz 500 WiFi Color Bulb with an approximated 800 Lumen at full intensity and the color temperature set to 5300K. I am using this bulb at 60% intensity for 2 x 5 hours with 2 hours rest in between. I guess that 1% intensity is about 300 Lumen and that it is now somewhere around 650 Lumen.
Can this problem be handled by giving the DOC longer and more intense periods of light and maybe even more daily food? The aquarium is standing 3 meters away from southwards facing windows. At the moment it is not directly touched by sunlight, but I guess it will in summer.