I created a new profile only once. I then copied the old directories and their contents (recursive) to the new profile, *not* the files (approx. 64) in the profile's root directory. Then I followed https://support.mozilla.org/en-US/kb/recovering-important-data-from-an-old-profile to get most of my settings back.
Good that the problem could be solved like this, although not nice that the problem appeared at all.
Thanks a lot for having taken the time for clarification!