Thank you both so much! I lost a whole day figuring out why my development system stopped working and how to get it running back again!
Thank you Jonatan for you hind. I already had 5.7 installed.
Thank’s John for your link and suggestion.
In the end it was enough to:
$ brew info mysql (to get info about the installed versions)
$ brew switch mysql 5.7.21 (to switch to a stable version)
I just could not believe that a full release could screw up my system.
Now the server, the mysql gems as well as connection are working again…
There was no need to uninstall mysql 8 in my case.
The point with MySQL is that I have to configure it so seldomly that when there is a problem I have always to start from scratch …