We have a lot of possible solutions now. Some work, some not.
Here is mine:
Unistall Creative Cloud Desktop (only this one, not the apps). -> CC Desktop uninstalled with errors. -> Unistall again -> CC Desktop uninstalled successfully !?
(Can't remember that I ever uninstalled a program twice. And I'm working with Windows for over 20 years - strange!)
Restart, Download and install CC Desktop, no further updates. But: After a few seconds with the Window open: Error message appears "No internet connection" -> Retry -> OK -> "No Internet connection" etc.
It looks like even this version is not the big success for us.