/usr/local/syncthing/var is the home directory of the syncthing user, but that location is not accessible via the DSM interface. You shouldn’t use it as a sync location, but instead, sync a shared folder or a dir inside a shared folder, something like that.
To allow Syncthing access to resources, you can set (RW) permissions for the sc-syncthing group in the DSM interface. Although you can’t actually see the syncthing user (system users are hidden), it is a member of that group.