Enable the CardDAV server feature on your Synology NAS and find out the CardDAV address. Here the manufacturer describes how this works.
Make sure that sync.blue® can reach your Synology via Internet (e.g. via Dynamic DNS with the provider ddnss.de).
Create a new connection in sync.blue® and select "CardDAV" as source or destination.
Store the URL to your CardDAV address book on your Synology device there. Example:
The use of QuickConnect-IDs is not supported!