Even more investigation: I found out that the working server had more php-packages installed. After installing them on the first one VisualEditor is running :) The necessary must be among them:
sudo apt install php-bz2 php-pear php-zip php-bcmath php-gmp php-pspell php-tidy
I have no clue which one was the missing one, but that should be pointed out in the install documentation.
