This is because it uses a QQC2.Toolbar which doesn't have the "you can drag me to move the window" feature implemented yet. We could fix this by either porting it to use a Kirigami [something]ApplicationHeader, or adding the requisite logic to our styling of QQC2.ToolBar. I slightly lean towards the latter.
Fixed with https://invent.kde.org/ngraham/welcome-app/-/commit/be9bb02896cdcf28f649be87be695097e8238ad0.