Ok. I was able to improve a bit my custom button for calling up the "Manage Cookies and Site Data" window. Both, the about:preferences#privacy and three seconds later the desired dialogue are now loaded in the same chrome window which avoids an additional loading of a tab. Nevertheless, I hope that there is a better solution yet.
As custom buttons are actually the topic of this thread, I have decided to post about this stuff here again. My project of creating a custom button to directly call up the "Manage Cookies and Site Data" dialogue in Mypal 68 seems to have come to a temporary end. It works perfectly. I have solved the issues encountered in my own way and I am currently in testing mode. Here is a short preview: