There's a couple ways you can do this. The latest revision of WSL lets you run Linux gui apps that appear in a x server window, and you can pin them to the taskbar/start menu. That is definitely using a built in x server.

Opening vscode in windows and opening the Linux vm's file through the "filesystem"(it's a network share) is unstable. You really have to open vscode in Linux, or run it in windows and ssh into the virtual machine for it to work well.