Since obviously nobody can help me, here is, what I found out so far.
First thing is, Calibre sets the ebook-directory to readonly for users, so I changed it recursively to 777. After that I could access the database with my PC-installation of calibre. Unfortunately from time to time occured database-write-errors, since two programs tried to access the database. Perhaps it would help to turn off calibre in omv each time before making changes. However, this is to laborious for me.
So I will maintain my main-calibre-database on my PC as I did before. And from time to time I copy the wohle ebook-directory (including the two database-files) to OMV: turn off Calibre in OMV, delete the whole content of the OMV-ebook-directory, copy everything and turn Calibre on again.
So I do not have the most recent version on the server, but I can do changes to the database. If someone finds a better solution, let me know