In order to add a directory to a Jellyfin library, it needs to access the directory and all its parent directories. So, if you add ~/Media to a library, Jellyfin fails to access it.
Permitting Access
To fix it, grant Jellyfin execution permission for your home directory. It runs as user jellyfin. setfacl --modify user:jellyfin:--x ~
Now, the media server can access not only ~/Media but also other directories under ~, which is unsafe.