The hint, that /etc/resolv.conf should probably point to
/run/systemd/resolve/resolv.conf was correct. The connection is back.
Now, my desktop (after being online again) sucks all the mail from my
mail provider, and places it in my local IMAP server (Dovecot). Which
doesn't work yet. There are problems with kmail. So, at the moment, I
don't have a working email connection any more. (Last, I've used a
I have to repair my mail connection, before I can answer any mail.