I only used something similar to mess around with Hytale modding a bit, but it was only easy because there was fully ready-to-use premade solution. But in general, if you're willing to go that way, I think the most simple option would be to create a distrobox with ubuntu/debian/fedora/arch (depending on which distro covers things you need better), install vs code there (using native package manager of given distribution), and then distrobox-export VS Code from that distrobox. Then you can simply manage everything inside of distrobox using full power of distribution you chose. To make things even better, distrobox has automatic passthrough of most hardware. For Nvidia in particular, you need to pass flag "--nvidia" when doing "distrobox-create". After that, you can even use game engines like Unity or Godot from distrobox with full GPU passthrough.

Well they basically forked Bazzite DX image and customized that... The hyprland fork author stopped maintaining it 8 months ago so it's not gonna work anymore with any recent Bazzite versions. So what they did is how Bazzite itself was created in the first place - by forking Fedora Atomic image and customizing it. I wouldn't really count this as "Bazzite supports other DE/WM", but yeah, if someone decided to go this far and make a fork like this then great, you can use it and hope they'll keep maintaining it.