Yeah, I think the best way of running VS Code is from within a toolbox. This way, you can use all the add-ons and such. But I only have one main development container. (And others for other stuff. Some people have multiple development containers, however, so this might not work as smoothly someone who does.)
Here’s a post I wrote about it back in 2019; it still holds up and is still what I do: SSH into a Toolbox - #4 by garrett
As noted in the comment, I copied the .desktop file from the toolbox to ~/.local/share/applications/ and edited the exec lines to prefix it with the toolbox command. This way, I can launch it from GNOME Shell too.
I have tried using a flatpak since, but it’s not quite right.
Meanwhile, Owen has another method too. Toolbox and Visual Studio Code Remote Containers (I haven’t tried it.)