Hi
Thanks for your reply.
Finally I was not able to manage it and I decided to take another approach :-\
I created the rescue admin account and noticed that I had no problems while login in with my AppleID and password, so I decided to move the folder of my former / normal account to OLD.<account> (mv /Users/<admin> /Users/OLD.<admin>
I created $HOME of the normal admin account again, but left it blank (just a mkdir /Users/<admin>) and changed ownership with chown to numeric id of normal admin account.
I logged out and logged in with the normal admin account.
I decided to copy same data from /Users/OLD.<admin>/Library but that gave other errors so I started over and decided to re-create email / internet accounts and so on (a lot of work ...).
The benefit of the work (so far): I got the impression Catalina is running much faster now, applications are responding much faster and everything is feeling more "versatile" (if that makes sense).
In comparison to my MBP the MacMini seems to be much faster now.
I have to say, that I upgraded to Catalina from Mountain Lion on (with Mavericks, Sierra and High Sierra in the meantime) - I think that's a second choice ... with a little bit of sadness I remember that I upgraded from ML to Mavericks without any problems, but while upgrading to Sierra then problems started and the Mini slowed down.
Hope this helps other people.
(of course I have to say that I am a UNiX administrator, so working with rsync, mv, tar, etc. is pretty familiar).
Regards, Dietmar