You made my day, burnout!
In the meantime, I had a remote session with an administrator and we already suspected that the security prefs were the critical point because KMail only worked when choosing SSL but not with TSL. After that I read your post and then new where to find these settings in Opera Mail (everything else you mentioned in your mail was fine). The big suprise was that the settings written down in my operaprefs.ini were:
Enable SSL v3=0 Enable TLS v1.1=0 Enable TLS v1.2=0
which looks like a very bad setting. I added the line for TLS v1.0 and set all TLSs to 1. Now mail sending works again!