I’m a C# developer and run .NET apps on Linux all the time. Even before .NET Core, I was using Mono to run C# apps on Linux. There used to be quite a few GNOME apps written in C#.
There’s .NET and then there’s .NET Core which is a mere subset of .NET.
Nope. The old .NET Framework has been deprecated for a long time. The latest version, 4.8.1, is not very different to 4.6 which was released 10 years ago.
The modern versions are just .NET, which is what .NET Core used to be, but with much more of the framework implemented in a cross-platform way.
The list of .NET stuff that will actually run on .NET Core (alone) is a barren wasteland.
All modern .NET code is built on the cross-platform framework. Only legacy apps used the old Windows-only .NET Framework.