It always show a about:blank page despite the configuration:

[Help]
ContextHelpOption=3
HomePage=qthelp://org.qt-project.qtdesignstudio.200/doc/studio-getting-started.html

As con already mentioned in the comments the welcome page context help isn't broken per se. It is more an issue of where the focus at the moment of pressing F1 is. If the user clicked into the top (Toolbar) or bottom (Statusbar) the welcome page hasn't focus so it won't show anything when context help will be called. When we would apply context help to the top and bottom bar then this context help would also be available through out the whole design studio as the top and bottom bars are always show. This might not be what we want especially due to the focus on those bars not really being visible. You can have focus on one of the bars, but at the same time a dock widget is focused (e.g. Navigator) expecting the dock widgets context help to trigger.