According to this article, I need to add the 'Desktop Experience'
feature before File Sync is available - however, I do not see that
Feature in the list of available features
When you install Windows Server 2016 using the Setup wizard, you can choose between Windows Server 2016 and Windows Server (Server with Desktop Experience). The Server with Desktop Experience option is the Windows Server 2016 equivalent of the Full installation option available in Windows Server 2012 R2 with the Desktop Experience feature installed. If you do not make a choice in the Setup wizard, Windows Server 2016 is installed; this is the Server Core installation option.
Unlike some previous releases of Windows Server, you cannot convert
between Server Core and Server with Desktop Experience after
installation. If you install Server with Desktop Experience and later
decide to use Server Core, you should do a fresh installation.
How can I get offline files to work in Server 2016?
From the doc the support in server OS was up to 2012R2 on what I see.
In case the doc lie, Just make sure the folder is set in CSC, not CA in example.
See the red checkbox in that picture:
Edit: striked the last reference, the share is not hosted on a windows.