The Firebird .NET provider is primarily developed for he Windows platform. The wire protocol implementation works with Mono and under Linux, so it can connect to a normal Firebird server.
The fbembed.dll
library for Firebird Embedded is specific to Windows and cannot be loaded on linux. The .NET provider code does have support for Linux, but it looks like you need to specifically compile it for linux. I assume the NuGet package is the default version compiled with support for Windows and Embedded.