In the past, you had to stick to a given version of the Python extension in Visual Studio Code in order to edit and/or debug Fusion 360 add-ins with it.
Now I've just run into the opposite problem in case of the latest update of Fusion 360: when using that version of the extension (i.e. version 2019.9.34911) the "Debug" and "Edit" buttons inside the "Scripts and Add-Ins" dialog of Fusion 360 stopped working.
The engineering team confirmed that now developers should be using the latest version of the Python extension in VS Code.
And indeed, that does work for me too 🎉