Hello,
after hours of searching and reading numerous posts on the topic e.g. https://unix.stackexchange.com/questions/354162/resilio-sync-wont-start-on-boot or https://bbs.archlinux.org/viewtopic.php?id=224363, checking ownership and permissions etc. I give up. At least I have learned some more linux basics.
Now I have installed the binary, added my Pro licence and everything works just fine. The only feature missing would be a start at booting. Maybe later