The info in that Stack Overflow answer is out of date as of last week (I'll post a new answer shortly). The "Inspect Widget" command was simple functionality that let you tap a widget in the app and have VS Code jump to the source code that created that widget.
In the current version of the VS Code plugin, there's integration with the Dart DevTools which include an inspector tree. The DevTools are still a preview, though already provide more functionality than the command above. You can launch them using the Dart: Open DevTools command, and there's a little more info here: