Update: we copied all files from the /home/user/MyDocs/ directory to a USB stick with rsync.
One file wasn't copied by rsync (/home/user/MyDocs/._?) - also tried to just cp it - but besides from that, all files and directories are the exact same on the USB stick as on the phone.
The car recognized the USB stick and immediately started playing the songs that are on it.
*puzzled*