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Based on your previous posts I assume that you use Windows as your server OS. I am sadly unable to help you with OS-level issues on Windows. I am also unfamiliar with the quirks of the Synology OS.
You can check if your *arr-apps run as the same user as the permissions on the share (on the *arr-server). The folder and contained files of the share on the Synology NAS should have read, write and execute (rwx) permissions for the user of the share.
The free downloads are slow, but as books are usually small, it is perfectly usable without donating.