The Linux connection manager was discontinued a few years back so I don't think you would be able to set up a current version on Linux as the host for the data files so someone using Sage 50 can access the database.

Right. Ok, so the connection manager must be running on Windows. It allows remote connections, so I was wondering if just the SDK is available for Linux. Then the Linux app would connect to the Windows connection manager. It would be simpler to just have the app running on Windows, but I was just wondering if a Linux version is available.

It's my understanding there has never been a Linux SDK, it has always been Windows because the Sage 50 software only runs on Windows.  The Linux Connection Manager for host files was discontinued with the 2015 release.

Unknown said:

Discontinuations

Linux is no longer supported as a file server for sharing company files. (Red Hat Enterprise Linux 5.0n and SUSE Linux Enterprise Server 10 were previously supported)

Sage has paid support available for the SDK, this peer forum is not the final answer on the subject.  My guess would be that if Visual Studio won't build targets for other platforms because of Windows-only precompiled DLLs, then there's no way.