itch.io

Yes, you can build EXE with VS Code, but that's a different animal 😅(and I don't know if it is easily possible to do on Linux. I never tried that, but you would need to do that using Wine I guess).
Normally you would use Visual Studio the full Windows only IDE (https://visualstudio.microsoft.com/vs/) and do it this way with the compilers and libraries Microsoft delivers for Windows.
In Visual Studio Code you have two options. Use Microsoft's compilers which came with the big Visual Studio solution what actually doesn't make sense why you would use VS Code then or you use a Linux environment for Windows and use the GCC for Windows in it  like Min-GW64 (https://www.mingw-w64.org/) or  MSYS2 (https://www.msys2.org/). These GCC for Windows act like the versions on Linux, but compile to Windows  EXE executables and instead of Linux ELF executables. I don't know if the makefiles in the source code are set up to compile to client binaries this way, but I know on Windows they compile the master server executable this way. Might be a bit fiddly to do it this way. In Visual Studio IDE it's just a simple "Build" click. Visual Studio IDE isn't lightweight. I guess the initial installation is around 14GB or more.