Most common cause of that message is that Steam client isn't running. Steam must be up and logged in before the API can initialize.
I assume it is running in your case and already logged in, so insure you are only initializing once.
Also for note we develop a Unity tool kit built on Steamworks.NET that is designed to make working with Steamworks easier ... you can use the Foundation for free ... which is Steamowrks.NET + managers and tools for the most common bits.
You can find it here ... it might help you out ... wont cost you anything and is based on Steamworks.NET so wont break anything you already have. https://assetstore.unity.com/packages/tools/integration/steamworks-foundation-151291
Also for note we develop a Unity tool kit built on Steamworks.NET that is designed to make working with Steamworks easier ... you can use the Foundation for free ... which is Steamowrks.NET + managers and tools for the most common bits.
You can find it here ... it might help you out ... wont cost you anything and is based on Steamworks.NET so wont break anything you already have. https://assetstore.unity.com/packages/tools/integration/steamworks-foundation-151291