On the bottom of my desktop I have a panel where I added starters f.e. for dolphin and firefox on the left end, besides the ApplicationMenu.

I did the same using Plasma 5.12 and found that clicking the Dolphin icon, the program is launched and an additional entry (broad tab) is added in the windowbar. This means, even having one or two instances of dolphin (same for firefox) running, the starter besides the ApplicationMenu is still available.

With Plasma 5.20 clicking the Dolphin icon replaces that starter with program entry (broad tab) and I cannot start a second instance from there.

Any idea, how I can get the older behavior back? Thank you, Michael.

You can middle click a task manager entry to open a new instance.

When dragging an application icon to the panel, it 'pins' it, and the icon turns into the taskbar 'block'.
Instead, right-click on an application in the main menu, and choose the 'Add to panel (widget)' option. This will add its icon that acts in the way that you want.

Thanks a lot, claydoh! That was my fault: I added the programs using "Add to Window Bar"; one must use "Add to Control Bar (Miniprogram)". Now I have it as desired.
Thanks and regards, Michael