Facepunch.Steamworks and Steamworks.NET both don’t work that well with Godot. One of them is pretty outdated and the other one doesn’t work correctly with NativeAOT.
The easiest solution is GodotSteam. Install it normally, as GDExtension for example. Afterwards you can use the C# bindings for it. You still might have to add a steam_appid.txt to your project root, but other than that the addon should take care of everything else, including copying the required API DLL files into the correct folder on export.
If you still want to use the Facepunch version, try placing the steam_api64.dll next to your Godot editor executable and make sure that the native library is compatible with the managed C# bindings. That should only work on Windows though.