I shipped a .NET Core product on a handful of Raspberry Pi's running whatever the current version of Debian was at the time. That's cross platform enough for me.
That's good to know, thank you. To help with the first part of my comment, upon which local system did you develop that product (and, I guess implied in that question is: was it just you, or were there other developers with their own workstation setups)?
Visual Studio on Windows 10. I don't know why you'd use anything else for a .NET project: it's by far the path of least resistance.
I was one of 3 developers but the others were writing iOS and Android apps that interfaced with my Web product. That said, they had identical setups. Since the code was hosted locally on the Pi and we were all remote, they needed to be able to build and deploy my code also.
Anecdotally, I've been using Visual Studio mostly regularly since the original ".NET Version" of Visual Studio (~2002), and I'm increasingly closing it and just using VS Code and the dotnet command line tools. Visual Studio is definitely starting to feel its age/weight and between all the C# 10 language features (finally) removing boilerplate (things like namespace statements and global usings), I'm often feeling more productive in VS Code than in full Visual Studio. For hobby projects I've moved entirely to VS Code even for .NET.
I'm inclined to imagine that with extensions like SSH remoting in VS Code you'd probably have a better Raspberry Pi deployment and debugging experience in VS Code than in Visual Studio, if you gave it a chance.