Finally. The problem was, that a sysadmin and a sysadmin are not the same.
The first sysadmin account on my mattermost installation I rarely used anymore after the installation and authorized my personal user as a sysadmin to do the admin work in sysconsole and so on.
Today I tried to login with the original admin account and acknowledged a bunch of “welcome to the new feature” windows - one of them for some kind of playbook news. After that I opened the system console and tried to change the system scheme again. This time without errors!
Long story short - also the update to (meanwhile) 7.8.0 was succesful and without errors.